Another expertise request

[Dr J R Stockton]

I have transcribed a paper by Euler on the three-body problem from PDF
to HTML and MathJax, with a parallel "translation" by Google.

That's an almost incomprehensible translation, of course; but it has
served to detect most of the typos in the transcription and to hint at
the meanings of the words used.

The Euler Archive has linked to it, as being better than the nothing
that they previously had.

It is at <http://www.merlyn.demon.co.uk/euler304.htm>.


Question 1.

In Sections 8 to 10 it talks about a situation with the Moon being four
times further away from us than it is, in conjunction or opposition.
That seems to be a discovery of two of the then-unknown Lagrange Points:

L3 Sun L1 Earth L2

Superior Inferior
Conjunction Conjunction Opposition

presumably, as four times, L1 and L2. Is that so? can those here tell
me, by reading without writing a translation, whether it does do, and
whether there is any mention of L3?


Question 2.

Would those here be good enough to contribute to the project a proper
translation of some or all of it? some of the numbered questions have
no or little maths, so should be easier to understand.

Granted, in the words of someone who helped with a translation of
Zeller, "that's not the sort of Latin that Caesar would have written".

--
(c) John Stockton, nr London, UK. Mail via homepage. Turnpike v6.05 MIME.
Web <http://www.merlyn.demon.co.uk/> - FAQqish topics, acronyms and links;
Astro stuff via astron-1.htm, gravity0.htm ; quotings.htm, pascal.htm, etc.

[Dr J R Stockton]

In alt.language.latin message <$SBAtubz...@invalid.uk.co.demon.merl
yn.invalid>, Mon, 10 Sep 2012 23:38:43, Dr J R Stockton <reply1237@merly
n.demon.co.uk.invalid> posted:

>I have transcribed a paper by Euler on the three-body problem from PDF
>to HTML and MathJax, with a parallel "translation" by Google.
>
>That's an almost incomprehensible translation, of course; but it has
>served to detect most of the typos in the transcription and to hint at
>the meanings of the words used.
>
>The Euler Archive has linked to it, as being better than the nothing
>that they previously had.
>
>It is at <http://www.merlyn.demon.co.uk/euler304.htm>.

No response. So I'll try another approach. How should the following
introductory sentence by the famous L. EULERO be translated (absolute
perfection is not a necessity; just a fair representation) ?

Etsi nullum est dubium, quin leges motus corporum coelestium a Keplero
observatae atque a Newtono confirmatae, Astronomiae maxima incrementa
attulerint, tamen nunc quidem certissimum est, nullum in coelo reperiri
corpus, quod leges istas in motu suo perfecte sequatur, cum potius in
omnibus haud leves aberrationes ab istis legibus deprehendantur.

I transcribe from two sources; a complete but hard to read c.18 PDF
"original", and a well-printed c.19? partially-visible imaged
transcription - their punctuation and spelling differ.

[Johannes Patruus]

On 15/09/2012 10:55, Dr J R Stockton wrote:
> In alt.language.latin message<$SBAtubz...@invalid.uk.co.demon.merl
> yn.invalid>, Mon, 10 Sep 2012 23:38:43, Dr J R Stockton<reply1237@merly
> n.demon.co.uk.invalid> posted:
>
>> I have transcribed a paper by Euler on the three-body problem from PDF
>> to HTML and MathJax, with a parallel "translation" by Google.
>>
>> That's an almost incomprehensible translation, of course; but it has
>> served to detect most of the typos in the transcription and to hint at
>> the meanings of the words used.
>>
>> The Euler Archive has linked to it, as being better than the nothing
>> that they previously had.
>>
>> It is at<http://www.merlyn.demon.co.uk/euler304.htm>.
>
> No response.

As you know, Usenet is dying on its feet, and there are very few people
left in this group, let alone people with the time and skill to translate
advanced scientific and mathematical texts.

> So I'll try another approach. How should the following
> introductory sentence by the famous L. EULERO be translated (absolute
> perfection is not a necessity; just a fair representation) ?
>
> Etsi nullum est dubium, quin leges motus corporum coelestium a Keplero
> observatae atque a Newtono confirmatae, Astronomiae maxima incrementa
> attulerint, tamen nunc quidem certissimum est, nullum in coelo reperiri
> corpus, quod leges istas in motu suo perfecte sequatur, cum potius in
> omnibus haud leves aberrationes ab istis legibus deprehendantur.
>
> I transcribe from two sources; a complete but hard to read c.18 PDF
> "original", and a well-printed c.19? partially-visible imaged
> transcription - their punctuation and spelling differ.

Well, OK, I'll have a go at it -

Although there is no doubt that the laws of motion of celestial bodies
observed by Kepler and confirmed by Newton have brought enormous gains to
astronomy, nevertheless it is now absolutely certain that there is no body
to be found in the heavens which perfectly follows those laws in its own
motion, since, on the contrary, non-trivial deviations from those laws are
observed in all of them.

Patruus

[Dr J R Stockton]

I think I failed to send this before.

In alt.language.latin message <abldam...@mid.individual.net>, Sun,
16 Sep 2012 08:27:19, Johannes Patruus <inv...@invalid.invalid> posted:

>On 15/09/2012 10:55, Dr J R Stockton wrote:
>> In alt.language.latin message<$SBAtubz...@invalid.uk.co.demon.merl
>> yn.invalid>, Mon, 10 Sep 2012 23:38:43, Dr J R Stockton<reply1237@merly
>> n.demon.co.uk.invalid> posted:

>>> It is at<http://www.merlyn.demon.co.uk/euler304.htm>.
>>
>> No response.
>
>As you know, Usenet is dying on its feet, and there are very few people
>left in this group, let alone people with the time and skill to
>translate advanced scientific and mathematical texts.

Indeed. But the art of writing such texts consists of using simple
words and grammar, except where technical terms are needed - and I know
those terms. It's the word order, the endings, and the common little
words that are a problem for me. After all, Euler was not writing for
Romans, but for educated Europeans of the day; and I think he knew how
to do it well.

>> So I'll try another approach. How should the following
>> introductory sentence by the famous L. EULERO be translated (absolute
>> perfection is not a necessity; just a fair representation) ?
>>
>> Etsi nullum est dubium, quin leges motus corporum coelestium a Keplero
>> observatae atque a Newtono confirmatae, Astronomiae maxima incrementa
>> attulerint, tamen nunc quidem certissimum est, nullum in coelo reperiri
>> corpus, quod leges istas in motu suo perfecte sequatur, cum potius in
>> omnibus haud leves aberrationes ab istis legibus deprehendantur.
>>
>> I transcribe from two sources; a complete but hard to read c.18 PDF
>> "original", and a well-printed c.19? partially-visible imaged
>> transcription - their punctuation and spelling differ.
>
>Well, OK, I'll have a go at it -
>
>Although there is no doubt that the laws of motion of celestial bodies
>observed by Kepler and confirmed by Newton have brought enormous gains
>to astronomy, nevertheless it is now absolutely certain that there is
>no body to be found in the heavens which perfectly follows those laws
>in its own motion, since, on the contrary, non-trivial deviations from
>those laws are observed in all of them.

I can see that, if Euler had been writing in English, he would have used
those words or very similar, had he been literate in English.

I've put that in Column 4, in a span titled (for pop-up) Patruus, and
will put my "translation" in that column on a yellow background. If you
want not to be named, I'll change that to the newsgroup name or URL

The next sentence, and perhaps someone else will translate it to spread
the burden, follows : the later part seems to state the inverse square
law.

Vera scilicet omnium motum coelestium causa in mutua horum corporum
attractione est posita, qua unumquodque ad singula reliqua urgetur
viribus rationem compositam ex directa simplici massarum, et inversa
duplicata distantiarum tenentibus.

Thanks for what you have done.

[Johannes Patruus]

No one else having put their head over the parapet, I'll have a try at
this sentence, though my understanding of it fades beyond the word
"viribus" (forces), with a concomitant descent of the translation into
semi-gibberish -

"The true cause of all celestial motions lies, of course, in the mutual
attraction of these bodies by which they are pushed towards each other by
forces holding a compound reckoning from the simple direct of the masses
and the inverse double of the distances."

Note 1 - The Latin "motum" should, I think, read "motuum", which latter is
the genitive plural.

Note 2 - The Latin "duplicata", at least in the classical lexicon, conveys
the notion of doubling rather than of squaring, for which one might have
expected "quadrata".

> Thanks for what you have done.

You're welcome.

Patruus

[Ed Cryer]

It's a problem of trying to get "directa simplici massarum" to mean "the
product of their masses"; and "inversa duplicata distantiarum" to mean
"inversely proportional to the square of the distance between them".

At first glance it can't be done. It says something different from that.
How does Newton state it in "Principia Mathematica"? Perhaps Euler was
misled by N's Latin.

Ed

[Johannes Patruus]

Google has just drawn our attention to these pages -
http://archive.org/stream/theoryofnaturalp00boscrich#page/162/mode/2up

in which -

"in ratione composita ex directa simplici massarum,
& reciproca duplicata distantiarum"

is rendered as -

"in the ratio compounded of the simple direct ratio of the masses
& the inverse duplicate ratio of the distances"

> Ed

Patruus

[Ed Cryer]

F = G*(m1m2/r²)

The opening sentence of the Praefatio of N's first edition Principia M is;
Cum Veteres Mechanicam (uti Author est Pappus) in verum Naturalium
investigatione maximi fecerint, & recentiores, missis formis
substantialibus & qualitatibus occultis, Phænomena Naturæ ad leges
Mathematicas revocare aggressi sint: Visum est in hoc Tractatu Mathesin
excolere quatenus ea ad Philosophiam spectat.
(Since the ancients (as we are told by Pappus), made great account of
the science of mechanics in the investigation of natural things; and the
moderns, laying aside substantial forms and occult qualities, have
endeavoured to subject the phaenomena of nature to the laws of
mathematics, I have in this treatise cultivated mathematics so far as it
regards philosophy.)

Brilliant! That sounds very modern.

Ed

[Dr J R Stockton]

In alt.language.latin message <abtfsk...@mid.individual.net>, Wed,
19 Sep 2012 10:00:24, Johannes Patruus <inv...@invalid.invalid> posted:

Undoubtedly. I copied the Latin with care, combining a fully legible
partial copy and a hard-to-read complete original; I used Google to
locate untranslatable and therefore probably erroneous words to be
emended; and I then checked carefully against the sources. But there
will be some errors left (I ought to have recognised that one, though).

>Note 2 - The Latin "duplicata", at least in the classical lexicon,
>conveys the notion of doubling rather than of squaring, for which one
>might have expected "quadrata".

Obviously the meaning is "squared"; I think the construction means
"proportional to (the inverse of the distance), twice" - and, earlier,
not exactly "proportional to (the product of the masses)", but
"proportional to one of the masses and also to the other of the masses".

In places, the "ordinary English" that best matches the Latin will need
re-translation into the English used by modern mathematicians,
physicists, astronomers, who are the intended readership. On that
basis, since attractions pull rather than push, I'll render "urgetur" as
"urged" rather than the linguistically-accurate "pushed".

So, copied from the fair copy now on the Web at
<http://www.merlyn.demon.co.uk/euler304.htm#Enestrom304>,
page 544 column 4,

"The true cause of all celestial motions lies, of course, in the

mutual attraction of these bodies by which they are urged

towards each other by forces holding a compound reckoning from

the product of the masses and the inverse square of the
distances."

That is intended to take account of subsequent articles up to about Sept
19th, 22:45 GMT, when I last collected News; and Google Groups shows no
others.

The next sentence is

"Semper autem commode usu venit, ut inter has vires una prae reliquis
maxime emineat, ideoque motus proxime regulis Keplerianis conformis,
evadat ; sicque effectus a reliquis oriundus veluti minimus per methodos
appropinquandi definiri possit."




My initial aim was to determine whether, in this document (the next one,
thankfully, is in French, and is better printed), Euler predicted any of
the Lagrange Points. Ideally, I'd have done it by reading an English
version via the Euler Archive at
<http://eulerarchive.maa.org/pages/E304.html> - but none is available.
(<http://eulerarchive.maa.org/pages/E327.html> does link to my version
of a later paper, and it will be nice if I can provide an adequate
version of E.304).

There is no suggestion of Euler discovering L4 & L5, the equilateral
configuration; and, if he had, I'm confident that I would have
recognised the inescapable words for equilateral or equiangular - if
looking in the right E-number.

For L1 L2 L3, the Pseudo-Moon is permanently in a straight line with Sun
and Earth and at a fixed position on that rotating line :

^
|
L1: Sun Earth PM
L2: Sun PM Earth
L3: PM Sun Earth
|
V

I think that, in Section 7, Euler refers to L1.
In section 8, Euler talks of an equation of the fifth degree, and I
assert that such an equation is used to locate L1 L2 L3.

Late in Page 550, "seu si Luna fere quater longius a nobis esset
remota,", a minor question : does he mean multiplying the Moon's
distance from Earth by 4, or adding an extra 4 times, making 5 times the
distance? 4 is a reasonable fit to the true value (5.5), but 5 would be
better.

But is there anything about L3, the "Counter-Earth" point? Probably not
after Section 10, since there the maths is too complicated for that.

Thanks for the continued help. I'm continuing to attack the easier-
looking parts of the later sections, among the maths.

--
(c) John Stockton, nr London, UK. For Mail, see Home Page. Turnpike, WinXP.
Web <http://www.merlyn.demon.co.uk/> - FAQ-type topics, acronyms, and links.
Command-prompt MiniTrue is useful for viewing/searching/altering files. Free,
DOS/Win/UNIX now 2.0.6; see <URL:http://www.merlyn.demon.co.uk/pc-links.htm>.

[Johannes Patruus]

When I was checking this point, the text Google found for me was this -
http://books.google.co.uk/books?id=CVejrSJ2Q18C&pg=PA247

By the way, in case it's of any interest, I've just noticed that numerous
links to Euler's works are to be found way down on this page -
http://www.philological.bham.ac.uk/bibliography/e.html

>> Note 2 - The Latin "duplicata", at least in the classical lexicon,
>> conveys the notion of doubling rather than of squaring, for which one
>> might have expected "quadrata".
>
> Obviously the meaning is "squared"; I think the construction means
> "proportional to (the inverse of the distance), twice" - and, earlier,
> not exactly "proportional to (the product of the masses)", but
> "proportional to one of the masses and also to the other of the masses".
>
> In places, the "ordinary English" that best matches the Latin will need
> re-translation into the English used by modern mathematicians,
> physicists, astronomers, who are the intended readership. On that
> basis, since attractions pull rather than push, I'll render "urgetur" as
> "urged" rather than the linguistically-accurate "pushed".

"Urged" is fine.

> So, copied from the fair copy now on the Web at
> <http://www.merlyn.demon.co.uk/euler304.htm#Enestrom304>,
> page 544 column 4,
>
> "The true cause of all celestial motions lies, of course, in the
> mutual attraction of these bodies by which they are urged
> towards each other by forces holding a compound reckoning from
> the product of the masses and the inverse square of the
> distances."
>
> That is intended to take account of subsequent articles up to about Sept
> 19th, 22:45 GMT, when I last collected News; and Google Groups shows no
> others.
>
> The next sentence is
>
> "Semper autem commode usu venit, ut inter has vires una prae reliquis
> maxime emineat, ideoque motus proxime regulis Keplerianis conformis,
> evadat ; sicque effectus a reliquis oriundus veluti minimus per methodos
> appropinquandi definiri possit."

"However it always conveniently happens that,
among these forces, one very greatly predominates[1] over the others,
so that the motion turns out to be closely conformable with Kepler's laws;
and thus the effect, as if minimal, arising from the other [forces]
can be determined through methods of approaching[2]."

[1] lit. stands out

[2] or, perhaps, "of approximating". Google's "the methods approach" is
suggestive of a technical term but sits less well with the Latin.

> My initial aim was to determine whether, in this document (the next one,
> thankfully, is in French, and is better printed), Euler predicted any of
> the Lagrange Points. Ideally, I'd have done it by reading an English
> version via the Euler Archive at
> <http://eulerarchive.maa.org/pages/E304.html> - but none is available.
> (<http://eulerarchive.maa.org/pages/E327.html> does link to my version
> of a later paper, and it will be nice if I can provide an adequate
> version of E.304).
>

> There is no suggestion of Euler discovering L4& L5, the equilateral

> configuration; and, if he had, I'm confident that I would have
> recognised the inescapable words for equilateral or equiangular - if
> looking in the right E-number.
>
> For L1 L2 L3, the Pseudo-Moon is permanently in a straight line with Sun
> and Earth and at a fixed position on that rotating line :
>
> ^
> |
> L1: Sun Earth PM
> L2: Sun PM Earth
> L3: PM Sun Earth
> |
> V
>
> I think that, in Section 7, Euler refers to L1.
> In section 8, Euler talks of an equation of the fifth degree, and I
> assert that such an equation is used to locate L1 L2 L3.
>
> Late in Page 550, "seu si Luna fere quater longius a nobis esset
> remota,", a minor question : does he mean multiplying the Moon's
> distance from Earth by 4, or adding an extra 4 times, making 5 times the
> distance? 4 is a reasonable fit to the true value (5.5), but 5 would be
> better.

Literally: "or if the moon were about four times more-distantly remote
from us".

> But is there anything about L3, the "Counter-Earth" point? Probably not
> after Section 10, since there the maths is too complicated for that.
>
> Thanks for the continued help. I'm continuing to attack the easier-
> looking parts of the later sections, among the maths.

Several decades ago I failed maths at A-level, since when it's been
downhill all the way!

Patruus

[Dr J R Stockton]

In alt.language.latin message <ac6obh...@mid.individual.net>, Sat,
22 Sep 2012 22:20:36, Johannes Patruus <inv...@invalid.invalid> posted:

>On 20/09/2012 20:02, Dr J R Stockton wrote:
>> In alt.language.latin message<abtfsk...@mid.individual.net>, Wed,
>> 19 Sep 2012 10:00:24, Johannes Patruus<inv...@invalid.invalid> posted:

>> Undoubtedly. I copied the Latin with care, combining a fully legible
>> partial copy and a hard-to-read complete original; I used Google to
>> locate untranslatable and therefore probably erroneous words to be
>> emended; and I then checked carefully against the sources. But there
>> will be some errors left (I ought to have recognised that one, though).
>
>When I was checking this point, the text Google found for me was this -
> http://books.google.co.uk/books?id=CVejrSJ2Q18C&pg=PA247

I know of that one - the book is "Leonhardi Euleri Commentationes
Astronomicae", which I assume is a 19th (or early 20th) century
printing. Google limits the number of pages visible; I've not seen
pp.246, 248, 251, 253, 258 (258 starts the next paper, in French, but
could have something about this one).

>By the way, in case it's of any interest, I've just noticed that
>numerous links to Euler's works are to be found way down on this page -
> http://www.philological.bham.ac.uk/bibliography/e.html

Alas, it lacks the Enestrom numbers.

Links such as
AUTHOR Euler, Leonhard (1707-1783)
TITLE Opera mathematica vol. 1.2.1
URL http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-
006952
SITE Gallica - Bibliothèque nationale de France
SUBJECT Mathematics
NOTES Dpr of the 1915 Leipzig edition; downloadable pdf form
look typographically rather like the previous reference.

>> So, copied from the fair copy now on the Web at
>> <http://www.merlyn.demon.co.uk/euler304.htm#Enestrom304>,
>> page 544 column 4,
>>
>> "The true cause of all celestial motions lies, of course, in the
>> mutual attraction of these bodies by which they are urged
>> towards each other by forces holding a compound reckoning from
>> the product of the masses and the inverse square of the
>> distances."
>>
>> That is intended to take account of subsequent articles up to about Sept
>> 19th, 22:45 GMT, when I last collected News; and Google Groups shows no
>> others.
>>
>> The next sentence is
>>
>> "Semper autem commode usu venit, ut inter has vires una prae reliquis
>> maxime emineat, ideoque motus proxime regulis Keplerianis conformis,
>> evadat ; sicque effectus a reliquis oriundus veluti minimus per methodos
>> appropinquandi definiri possit."
>
>"However it always conveniently happens that,
>among these forces, one very greatly predominates[1] over the others,
>so that the motion turns out to be closely conformable with Kepler's laws;
>and thus the effect, as if minimal, arising from the other [forces]
>can be determined through methods of approaching[2]."
>
>[1] lit. stands out

Your version sounds a bit like piling Pelion upon Ossa twice !! But it
gives a clear meaning.

>
>[2] or, perhaps, "of approximating". Google's "the methods approach" is
>suggestive of a technical term but sits less well with the Latin.

"through methods of approximation.". Approximation is the word in
general use for such.

>> Late in Page 550, "seu si Luna fere quater longius a nobis esset
>> remota,", a minor question : does he mean multiplying the Moon's
>> distance from Earth by 4, or adding an extra 4 times, making 5 times the
>> distance? 4 is a reasonable fit to the true value (5.5), but 5 would be
>> better.
>
>
>Literally: "or if the moon were about four times more-distantly remote
>from us".

Yes, but does that mean a total of 4 or of 5? I can leave that as an
exercise for the reader.

>Several decades ago I failed maths at A-level, since when it's been
>downhill all the way!

I learned Latin twice, at about the same time; but it wears off.
Perhaps I should complete my collection of "Asterix le Gaulois" in
Latin.


It's getting very late; the next sentence, completing section 1, must
wait for tomorrow.

Again thanks.

--
(c) John Stockton, nr London, UK. ?@merlyn.demon.co.uk Turnpike v6.05.
Website <http://www.merlyn.demon.co.uk/> - w. FAQish topics, links, acronyms
PAS EXE etc. : <http://www.merlyn.demon.co.uk/programs/> - see in 00index.htm
Dates - miscdate.htm estrdate.htm js-dates.htm pas-time.htm critdate.htm etc.

[Dr J R Stockton]

SECOND FOLLOW_UP

In alt.language.latin message <ac6obh...@mid.individual.net>, Sat,

22 Sep 2012 22:20:36, Johannes Patruus <inv...@invalid.invalid> posted:

>On 20/09/2012 20:02, Dr J R Stockton wrote:
>> In alt.language.latin message<abtfsk...@mid.individual.net>, Wed,
>> 19 Sep 2012 10:00:24, Johannes Patruus<inv...@invalid.invalid> posted:

>>> Note 2 - The Latin "duplicata", at least in the classical lexicon,
>>> conveys the notion of doubling rather than of squaring, for which one
>>> might have expected "quadrata".
>>
>> Obviously the meaning is "squared"; I think the construction means
>> "proportional to (the inverse of the distance), twice" - and, earlier,
>> not exactly "proportional to (the product of the masses)", but
>> "proportional to one of the masses and also to the other of the masses".

I happened to be reading, before breakfast today, Volume 1 (Books I &
II) of "Euclid / the thirteen books of The Elements", 2nd edition, by
Sir Thomas L Heath, pub. Dover, supplier Oxfam, and reached the last
paragraph of "Additional Axioms", in Book 1 : Notes and Definitions,
etc., page 234.

Heath quotes Archimedes : "... they have proved that circles have to one
another the duplicate ratio of their diameters, that spheres have to one
another the triplicate ratio of their diameters, and so on.". So
Euler's usage has sufficiently illustrious precedent.

If anyone sees Vols 2 or 3 of Heath in their local Oxfam, please ask for
one copy to be moved to the New Malden branch.

Also, a Google search for "duplicate ratio"... - and Wikipedia "Ratio"
implies that Euclid Book V Definition 8 defines that term.

>> Late in Page 550, "seu si Luna fere quater longius a nobis esset

>> remota, ...

Actually, fairly late on page 549.

>> Thanks for the continued help. I'm continuing to attack the easier-
>> looking parts of the later sections, among the maths.

For the purposes of translation, it is sufficient to consider each
mathematical chunk (possibly separated by internal punctuation) as a
different unknown noun of a fictitious declension; or as anything else
that may be demanded by context. If it has no "=", then it is an
expression; otherwise it is an equation. E&OE.


The "result" page, <http://www.merlyn.demon.co.uk/euler304.htm> , now
has (for ease of reference) each table row numbered decimally, the
fractional part subdividing Euler's section-numbering.

That page is now cited, presently as a transcription, at
<http://eulerarchive.maa.org/pages/E304.html>.

I now have approximate translations of a modest proportion of the later
sections installed (yellow background) in the final column.


The speed with which the maths in that page is rendered is considerably
browser-dependent; so if expecting to look at that page frequently it is
well to see which of one's browsers is fastest. For me, with WinXP pro
sp3, Chrome is good, but Safari 5.1.7 (no longer available) is best.


The next sentence, completing Euler section 1, is

"Quod nisi eveniret, in maxima adhuc ignoratione motuum coelestium
versaremur, cum nulla methodus adhuc sit inventa, cuius ope trium saltem
corporum se mutuo attrahentium motus assignari queat ; nisi forte una
vis caeteras plurimum superet."

There, "trium corporum" will be "three bodies", an established term.

--

[Johannes Patruus]

On 23/09/2012 23:39, Dr J R Stockton wrote:

>>> Late in Page 550, "seu si Luna fere quater longius a nobis esset
>>> remota,", a minor question : does he mean multiplying the Moon's
>>> distance from Earth by 4, or adding an extra 4 times, making 5 times the
>>> distance? 4 is a reasonable fit to the true value (5.5), but 5 would be
>>> better.
>>
>> Literally: "or if the moon were about four times more-distantly remote
>>from us".
>
> Yes, but does that mean a total of 4 or of 5? I can leave that as an
> exercise for the reader.

From the plain meaning of the words I would have said 4, but we seem to
be dealing with an author whose words do not always unambiguously convey
what he means. If he had intended 5 he could easily have expressed this by
substituting "quinquiens" (five times) for "quater".

>> Several decades ago I failed maths at A-level, since when it's been
>> downhill all the way!
>
> I learned Latin twice, at about the same time; but it wears off.
> Perhaps I should complete my collection of "Asterix le Gaulois" in
> Latin.

Third time lucky would make you a polymath, and how few of those there are
in the modern world!

> It's getting very late; the next sentence, completing section 1, must
> wait for tomorrow.
>
> Again thanks.

You're welcome.

Patruus

[Johannes Patruus]

Amazon-UK has the Dover paperbacks of vol.2 (464pp.) and vol.3 (574pp.)
for GBP 9.17 and 8.31 respectively, with even cheaper buying options
provided from other suppliers.

> Also, a Google search for "duplicate ratio"... - and Wikipedia "Ratio"
> implies that Euclid Book V Definition 8 defines that term.
>
>
>
>>> Late in Page 550, "seu si Luna fere quater longius a nobis esset
>>> remota, ...
>
> Actually, fairly late on page 549.
>
>
>>> Thanks for the continued help. I'm continuing to attack the easier-
>>> looking parts of the later sections, among the maths.
>
>
> For the purposes of translation, it is sufficient to consider each
> mathematical chunk (possibly separated by internal punctuation) as a
> different unknown noun of a fictitious declension; or as anything else
> that may be demanded by context. If it has no "=", then it is an
> expression; otherwise it is an equation. E&OE.

E&OE? Are you selling insurance policies?

> The "result" page,<http://www.merlyn.demon.co.uk/euler304.htm> , now
> has (for ease of reference) each table row numbered decimally, the
> fractional part subdividing Euler's section-numbering.
>
> That page is now cited, presently as a transcription, at
> <http://eulerarchive.maa.org/pages/E304.html>.
>
> I now have approximate translations of a modest proportion of the later
> sections installed (yellow background) in the final column.
>
>
> The speed with which the maths in that page is rendered is considerably
> browser-dependent; so if expecting to look at that page frequently it is
> well to see which of one's browsers is fastest. For me, with WinXP pro
> sp3, Chrome is good, but Safari 5.1.7 (no longer available) is best.
>
>
> The next sentence, completing Euler section 1, is
>
> "Quod nisi eveniret, in maxima adhuc ignoratione motuum coelestium
> versaremur, cum nulla methodus adhuc sit inventa, cuius ope trium saltem
> corporum se mutuo attrahentium motus assignari queat ; nisi forte una
> vis caeteras plurimum superet."
>
> There, "trium corporum" will be "three bodies", an established term.

I will endeavour to contribute a translation in a separate post by tomorrow.

Patruus

[Ed Cryer]

May I jump in and offer a translation? It will at least perform the
service of a straw man.

"Quod nisi eveniret, in maxima adhuc ignoratione motuum coelestium
versaremur, cum nulla methodus adhuc sit inventa, cuius ope trium saltem
corporum se mutuo attrahentium motus assignari queat ; nisi forte una
vis caeteras plurimum superet."

If this were not the case then we would still be extremely ignorant of
the motions of the heavens, since no method has as yet been found by
which the motion of three or more mutually attracting bodies can be
assigned; unless perchance one force be vastly superior to the others.

Incidentally, my instinct on "seu si Luna fere quater longius a nobis
esset remota," is different from yours. What jumps to mind is the
difference between two English expressions; four times longer and four
times as long; the first implying 5, the latter 4. And I think I can
distinguish between them in Latin as follows;
logius quater quam ....
tam longum quater quam ...
But I can't prove it. And the fact that your instinct about the English
is different from mine leaves me unsure; as well as the fact that
Euler's Latin has other wayward tendencies.

Ed

[Johannes Patruus]

The more the merrier!

> "Quod nisi eveniret, in maxima adhuc ignoratione motuum coelestium
> versaremur, cum nulla methodus adhuc sit inventa, cuius ope trium saltem
> corporum se mutuo attrahentium motus assignari queat ; nisi forte una
> vis caeteras plurimum superet."
>
> If this were not the case then we would still be extremely ignorant of the
> motions of the heavens, since no method has as yet been found by which the
> motion of three or more mutually attracting bodies can be assigned; unless
> perchance one force be vastly superior to the others.

That's very similar to my draft -

Were it not so,
we would still be in the greatest ignorance of heavenly motions,

since no method has as yet been found

with whose help
the motion of at least three mutually attracting bodies can be assigned,
unless it should happen than one force very much surpass the others.

> Incidentally, my instinct on "seu si Luna fere quater longius a nobis
> esset remota," is different from yours. What jumps to mind is the
> difference between two English expressions; four times longer and four
> times as long; the first implying 5, the latter 4. And I think I can
> distinguish between them in Latin as follows;
> logius quater quam ....
> tam longum quater quam ...
> But I can't prove it. And the fact that your instinct about the English is
> different from mine leaves me unsure; as well as the fact that Euler's
> Latin has other wayward tendencies.

The whole thing seems to be mired in ambiguity, and I can't think about it
any more without the risk of sending myself doolally -
http://www.englishforums.com/English/ThreeTimesAsSmallAs/whdlc/post.htm

> Ed

Patruus Non-Doolalliturus

[Ed Cryer]

Sheesh! Angels fear to tread .....

Well, at least it's not got to do with the p word. I've just listened to
a woman on BBC News explaining the origins of it in the class-battles of
the old Roman Republic; then on to Coriolanus.
No, not the p word!

Ed

[Johannes Patruus]

Archbishop Cranmer gives the ashes a thoughtful raking over -
http://archbishop-cranmer.blogspot.co.uk/2012/09/andrew-mitchell-has-to-go-for-good-of.html

as does Peter Hitchens -
http://hitchensblog.mailonsunday.co.uk/2012/09/street-of-shame-.html

[Memo to OP - Please excuse us while we go OT.]

> Ed

Patruus

[Dr J R Stockton]

In alt.language.latin message <acb5ie...@mid.individual.net>, Mon,
24 Sep 2012 14:29:56, Johannes Patruus <inv...@invalid.invalid> posted:

>On 24/09/2012 12:01, Dr J R Stockton wrote:
>> SECOND FOLLOW_UP
>>
>> In alt.language.latin message<ac6obh...@mid.individual.net>, Sat,
>> 22 Sep 2012 22:20:36, Johannes Patruus<inv...@invalid.invalid> posted:
>>> On 20/09/2012 20:02, Dr J R Stockton wrote:
>>>> In alt.language.latin message<abtfsk...@mid.individual.net>, Wed,
>>>> 19 Sep 2012 10:00:24, Johannes Patruus<inv...@invalid.invalid> posted:

>> I happened to be reading, before breakfast today, Volume 1 (Books I&
>> II) of "Euclid / the thirteen books of The Elements", 2nd edition, by
>> Sir Thomas L Heath,

>> If anyone sees Vols 2 or 3 of Heath in their local Oxfam, please ask for
>> one copy to be moved to the New Malden branch.
>
>Amazon-UK has the Dover paperbacks of vol.2 (464pp.) and vol.3 (574pp.)
>for GBP 9.17 and 8.31 respectively, with even cheaper buying options
>provided from other suppliers.

I'm both mean and low on bookshelf-space, and prefer to see before
buying - the charity shops in the High Street have done me better than
the one part-bookshop we used to have, together with a rather small WHS.
But I've felt that temptation, and have seen those on Amazon. I wonder
what the Danes use instead, there apparently being no amazon.dk, as I
get amazon.co.uk instead (which lacks the book).

>> The "result" page,<http://www.merlyn.demon.co.uk/euler304.htm> , now
>> has (for ease of reference) each table row numbered decimally, the
>> fractional part subdividing Euler's section-numbering.

>> I now have approximate translations of a modest proportion of the later
>> sections installed (yellow background) in the final column.

Now a grey background, with yellow reserved for my comment. That
proportion is considerably increased.

[Dr J R Stockton]

In alt.language.latin message <acbpjq...@mid.individual.net>, Mon,
24 Sep 2012 20:12:06, Johannes Patruus <inv...@invalid.invalid> posted:

>On 24/09/2012 18:40, Ed Cryer wrote:
>> Johannes Patruus wrote:

>> "Quod nisi eveniret, in maxima adhuc ignoratione motuum coelestium
>> versaremur, cum nulla methodus adhuc sit inventa, cuius ope trium saltem
>> corporum se mutuo attrahentium motus assignari queat ; nisi forte una
>> vis caeteras plurimum superet."
>>
>> If this were not the case then we would still be extremely ignorant of the
>> motions of the heavens, since no method has as yet been found by which the
>> motion of three or more mutually attracting bodies can be assigned; unless
>> perchance one force be vastly superior to the others.
>
>That's very similar to my draft -
>
>Were it not so,
>we would still be in the greatest ignorance of heavenly motions,
>since no method has as yet been found
>with whose help
>the motion of at least three mutually attracting bodies can be assigned,
>unless it should happen than one force very much surpass the others.

Both seem to me to have the same meaning, and to be compatible with the
situation when Euler was writing, etc.; I've taken Ed's, out of a
feeling of fairness.


That completes Section 1; sections 2, 3, 4 are equally introductory, and
I've done half of Section 3 in grey, and much of 5-9 likewise.


The first considerable gap is Section 10; it is a single paragraph free
of equations, but seems to contain some of what most interests me. In
this case it seems best to present the whole short section for
translation as a whole or a sentence at a time, since the translation of
a sentence in it may be aided by a sight of what other sentences are
saying.

Conjunction and opposition are anciently-established relevant technical
terms : <http://en.wikipedia.org/wiki/Conjunction_%28astronomy_and_astro
logy%29#Superior_and_inferior>. Admittedly that is for inner and outer
planets. For the locations of interest in the Sun-Earth system, L1 is
New Moon (may be eclipsing), L2 is Full Moon (may be eclipsed). L3 is
Philolaus' Counter-Earth <http://en.wikipedia.org/wiki/Counter-Earth>.

I now suspect that the work reveals L1 & L2, but not L3.


10. Casus hi eo magis sunt notatu digni, quod sine ulla approximatione
absolute expediri possunt, etiamsi ambae vires Solis et terrae ad motum
producendum concurrant, id quo nullo alio casu praestare licet.

Tali autem motu simplici corpus re vera moveretur, si ipsi in distanta
assignata, dum Soli, vel coniunctum, vel oppositum, ex terra appareret,
eiusmodi motus imprimeretur, ut cum terra pari passu in plano eclipticae
ingredi inciperet.

Sin autem motus impressus tantillum ab hac lege discrepet, non quidem
perpetuo Soli, vel coniunctum, vel oppositum, maneret, sed exiguas
excursiones hinc inde quasi oscillando conficeret.

Quo casu cum motus minime ab inventa ratione esset discrepaturus, more
solito, approximando etiam, eiusmodi motum definire licebit; in quo cum
quasi initium motuum irregularium, quos nullo etiamnum modo ad calculum
revocare licet, conspiciatur, usu certe non carebit, si in naturam
istiusmodi motuum accuratius inquisivero.


--

[Ed Cryer]

Dr J R Stockton wrote:

Believe it or not but I think I've come up with a fair translation of
this. There is, however, one crucial question. The meaning of the phrase
"in distanta assignata" will alter immeasurably from the addition of one
little iota; "distantIa".
Double check your original source, and let us know.

Ed

[Johannes Patruus]

Well good, because it's had me floundering like a beached octopus!

> There is, however, one crucial question. The meaning of the phrase
> "in distanta assignata" will alter immeasurably from the addition of one
> little iota; "distantIa".
> Double check your original source, and let us know.

It's "distantia" here -
http://books.google.co.uk/books?id=CVejrSJ2Q18C&pg=PA252

Also, "id quo" in the first para should apparently be "id quod"

> Ed

Patruus

[Ed Cryer]

Not easy by any means; and even less so for little me who only scraped
through GCSE O Level Maths by the skin of my teeth.

I hope I'm not suffering from an attack of overweening self confidence.
I once had a strong tendency theretoward. Someone once told me I
suffered from an as-yet unrecognised mental disorder; the opposite of an
inferiority complex - a superiority complex. I'm the intellectual
equivalent and parallel of Ranulph Fiennes (God bless his soul in the
Antarctic wastes! If anybody deserves to survive that then it's him).

I'd appreciate your approval of this translation before the good Doctor
starts to take it as sanctioned.

**********************

10. Casus hi eo magis sunt notatu digni, quod sine ulla approximatione
absolute expediri possunt, etiamsi ambae vires Solis et terrae ad motum

producendum concurrant, id quod nullo alio casu praestare licet.

These cases are all the more worthy of mention since they can be worked
out absolutely without any approximising, even if both forces of Sun and
Earth act together in producing motion, something which cannot be
maintained in any other case.

Tali autem motu simplici corpus re vera moveretur, si ipsi in distantia

assignata, dum Soli, vel coniunctum, vel oppositum, ex terra appareret,
eiusmodi motus imprimeretur, ut cum terra pari passu in plano eclipticae
ingredi inciperet.

But by such a simple motion a body would really be moved, if to it at a
fixed distance, while it appeared from earth either in conjunction or
opposition to the Sun, a motion were impressed of such kind that it
began to go at the same pace with the earth in the plane of the ecliptic.

Sin autem motus impressus tantillum ab hac lege discrepet, non quidem
perpetuo Soli, vel coniunctum, vel oppositum, maneret, sed exiguas
excursiones hinc inde quasi oscillando conficeret.

But if the impressed motion varied a fraction from this law, it would
remain not perpetually in conjunction or opposition to the Sun, but
would effect tiny excursions as if swinging here and there.

Quo casu cum motus minime ab inventa ratione esset discrepaturus, more
solito, approximando etiam, eiusmodi motum definire licebit; in quo cum
quasi initium motuum irregularium, quos nullo etiamnum modo ad calculum
revocare licet, conspiciatur, usu certe non carebit, si in naturam
istiusmodi motuum accuratius inquisivero.

In a case where the motion differed minimally from the discovered
formula, in the usual way, also by approximating, it will be possible to
define such motion; in which when an apparent beginning of irregular
motions be observed, which motions cannot be aligned at all as yet with
any calculation, that motion will not lack usefulness if I inquire
deeper into the nature of such motions.




Ed

[Johannes Patruus]

I have tended to suffer from the reverse syndrome since various failures
at university made me aware of my own limitations. It is only recently, on
rediscovering my ability to play moderately difficult stuff on the piano,
that have I started to feel a bit more positive!

I go along with your first three sentences, but in the fourth it is rather
difficult to discern the hierarchy of the clauses, or even to be sure what
the sentence's principal clause is (ditto in the Latin).

Other queries about this sentence -
(a) Could "Quo casu cum ..." be "In which case, since ..."?
(b) What is the antecedent of the second Latin "quo"?
(c) Could "usu certe non carebit ..." be "it will surely not be without
advantage if ..."?

I am now too tired to puzzle over this any more today.

> Ed

Patruus

[Ed Cryer]

(a) I thought the use of the imperfect subjunctive in the protasis and
the future indicative in the apodosis favoured my translation.
It's all about which "case" is being referred to; the one in the
previous sentence, or the one following in this one. Both seem similar
to me, but I'm no mathematician. "Eo casu quo" easliy transmutes to "quo
casu ubi (cum)".
It's a toss-up then between "In which case since the motion would differ
minimally from ..." and "In a case where the motion were to differ
minimally from .....". I'll leave that to a mathematician to decide.

(b) I took it as either the case outlined or the motion mentioned;
ambiguous in the Latin, hence my simple "in which".

(c) Maybe you're right; impersonal usage of "carebit". I've altered my
translation accordingly
In a case where the motion were to differ minimally from the discovered

formula, in the usual way, also by approximating, it will be possible to
define such motion; in which when an apparent beginning of irregular
motions be observed, which motions cannot be aligned at all as yet with

any calculation, it will surely not lack usefulness if I inquire deeper

into the nature of such motions.

Ed

[Johannes Patruus]

That, I confess, had not occurred to me.

> It's a toss-up then between "In which case since the motion would differ
> minimally from ..." and "In a case where the motion were to differ
> minimally from .....". I'll leave that to a mathematician to decide.
>
> (b) I took it as either the case outlined or the motion mentioned;
> ambiguous in the Latin, hence my simple "in which".
>
> (c) Maybe you're right; impersonal usage of "carebit". I've altered my
> translation accordingly

> In a case where the motion were to differ minimally from the discovered
> formula, in the usual way, also by approximating, it will be possible to
> define such motion; in which when an apparent beginning of irregular
> motions be observed, which motions cannot be aligned at all as yet with
> any calculation, it will surely not lack usefulness if I inquire deeper
> into the nature of such motions.

Now we can rest our bones till the OP replies.

> Ed

Patruus

[Dr J R Stockton]

In alt.language.latin message <k3v61u$qfr$1...@dont-email.me>, Wed, 26 Sep
2012 16:11:48, Ed Cryer <e...@somewhere.in.the.uk> posted:

>Believe it or not but I think I've come up with a fair translation of
>this. There is, however, one crucial question. The meaning of the
>phrase "in distanta assignata" will alter immeasurably from the
>addition of one little iota; "distantIa".
>Double check your original source, and let us know.

Both sources agree that you are right : distantia.


My <http://www.merlyn.demon.co.uk/euler304.htm> contains not only all
that is so far done : transcription, Google translate, human translate -
but also links to the sources used.

--
(c) John Stockton, Surrey, UK. ?@merlyn.demon.co.uk Turnpike v6.05 MIME.
Web <http://www.merlyn.demon.co.uk/> - FAQish topics, acronyms, & links.
Proper <= 4-line sig. separator as above, a line exactly "-- " (SonOfRFC1036)
Do not Mail News to me. Before a reply, quote with ">" or "> " (SonOfRFC1036)

[Dr J R Stockton]

In alt.language.latin message <acglir...@mid.individual.net>, Wed,
26 Sep 2012 16:34:23, Johannes Patruus <inv...@invalid.invalid> posted:

>
>It's "distantia" here -
> http://books.google.co.uk/books?id=CVejrSJ2Q18C&pg=PA252
>
>Also, "id quo" in the first para should apparently be "id quod"

Agreed.

Page 246 of that reference is apparently part of an Abstract, the rest
of which I have found. The whole Abstract is now transcribed, but not
properly checked, in <http://www.merlyn.demon.co.uk/euler304.htm>.

--
(c) John Stockton, near London. Mail ?.?.Stoc...@physics.org
Web <http://www.merlyn.demon.co.uk/> - FAQish topics, acronyms, and links.

[Dr J R Stockton]

In alt.language.latin message <k3v9fb$hv6$1...@dont-email.me>, Wed, 26 Sep
2012 17:10:01, Ed Cryer <e...@somewhere.in.the.uk> posted:

>
>I'd appreciate your approval of this translation before the good Doctor
>starts to take it as sanctioned.
>
>**********************
>
> 10. Casus hi eo magis sunt notatu digni, quod sine ulla approximatione
>absolute expediri possunt, etiamsi ambae vires Solis et terrae ad motum
>producendum concurrant, id quod nullo alio casu praestare licet.
>
>These cases are all the more worthy of mention since they can be worked
>out absolutely without any approximising, even if both forces of Sun
>and Earth act together in producing motion, something which cannot be
>maintained in any other case.

It makes MUCH more sense than Google Translate does; and it fits well
with the overall story as I am now beginning to perceive it better
(except that I doubt whether the word "approximising" exists <g>).

I will, as suggested, await a final verdict. Thanks.

--

[Dr J R Stockton]

In alt.language.latin message <GZT+PeFR...@invalid.uk.co.demon.merl
yn.invalid>, Thu, 27 Sep 2012 20:52:49, Dr J R Stockton <reply1239@merly
n.demon.co.uk.invalid> posted:

>In alt.language.latin message <acglir...@mid.individual.net>, Wed,
>26 Sep 2012 16:34:23, Johannes Patruus <inv...@invalid.invalid> posted:
>
>>
>>It's "distantia" here -
>> http://books.google.co.uk/books?id=CVejrSJ2Q18C&pg=PA252
>>
>>Also, "id quo" in the first para should apparently be "id quod"
>
>Agreed.
>
>Page 246 of that reference is apparently part of an Abstract, the rest
>of which I have found. The whole Abstract is now transcribed, but not
>properly checked, in <http://www.merlyn.demon.co.uk/euler304.htm>.

A generally much better rendition of the whole is in (scan of book)

<http://archive.org/stream/novicommentariac10impe">

Novi commentarii Academiae scientiarum imperialis petropolitanae, Tom.
X., pro Anno MDCCLXIV (1766)
E.304 : Abstract, pp.66-67, #page/n71; Index entry, #page/n75; Article,
p.544-558, #page/544; Figure, #page/n677, upper.

With a single mouse-click, the whole book can be heard, after a fashion.


BTW : the original contains "desudasse", once in the Abstract and once
in the Article. Google Translate disliked it, but liked "de sudasse" as
meaning "sweated out", which fits. Comment?

--
(c) John Stockton, nr London UK. Mail via Homepage DOS 3.3, 6.20; WinXP, 7.
Web <http://www.merlyn.demon.co.uk/> - FAQqish topics, acronyms and links.
PAS EXE TXT ZIP via <http://www.merlyn.demon.co.uk/programs/00index.htm>
My DOS <http://www.merlyn.demon.co.uk/batfiles.htm> - also batprogs.htm.

[Johannes Patruus]

On 28/09/2012 23:29, Dr J R Stockton wrote:
> In alt.language.latin message<GZT+PeFR...@invalid.uk.co.demon.merl
> yn.invalid>, Thu, 27 Sep 2012 20:52:49, Dr J R Stockton<reply1239@merly
> n.demon.co.uk.invalid> posted:
>
>> In alt.language.latin message<acglir...@mid.individual.net>, Wed,
>> 26 Sep 2012 16:34:23, Johannes Patruus<inv...@invalid.invalid> posted:
>>
>>>
>>> It's "distantia" here -
>>> http://books.google.co.uk/books?id=CVejrSJ2Q18C&pg=PA252
>>>
>>> Also, "id quo" in the first para should apparently be "id quod"
>>
>> Agreed.
>>
>> Page 246 of that reference is apparently part of an Abstract, the rest
>> of which I have found. The whole Abstract is now transcribed, but not
>> properly checked, in<http://www.merlyn.demon.co.uk/euler304.htm>.
>
>
> A generally much better rendition of the whole is in (scan of book)
>
> <http://archive.org/stream/novicommentariac10impe">
>
> Novi commentarii Academiae scientiarum imperialis petropolitanae, Tom.
> X., pro Anno MDCCLXIV (1766)
> E.304 : Abstract, pp.66-67, #page/n71; Index entry, #page/n75; Article,
> p.544-558, #page/544; Figure, #page/n677, upper.
>
> With a single mouse-click, the whole book can be heard, after a fashion.
>
>
> BTW : the original contains "desudasse", once in the Abstract and once
> in the Article. Google Translate disliked it, but liked "de sudasse" as
> meaning "sweated out", which fits. Comment?

"Desudasse" is a contracted form of "desudavisse" which is the perfect
active infinitive of "desudo", which is a verb compounded from "de-" +
"sudo", the compounded and uncompounded verbs being of similar sudatory
significance, the former including an intensified meaning of the latter.

References -

http://lysy2.archives.nd.edu/cgi-bin/words.exe?desudasse

http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0059%3Aentry%3Ddesudo

http://www.perseus.tufts.edu/hopper/text?doc=sudo&fromdoc=Perseus%3Atext%3A1999.04.0059

The following two search pages are worth bookmarking -
http://lysy2.archives.nd.edu/cgi-bin/words.exe
http://www.perseus.tufts.edu/hopper/resolveform?lang=latin

Patruus

[B. T. Raven]

Die Fri Sep 28 2012 17:29:03 GMT-0500 (Central Daylight Time) Dr J R
Stockton <repl...@merlyn.demon.co.uk.invalid> scripsit:

> In alt.language.latin message <GZT+PeFR...@invalid.uk.co.demon.merl
> yn.invalid>, Thu, 27 Sep 2012 20:52:49, Dr J R Stockton <reply1239@merly
> n.demon.co.uk.invalid> posted:
>
>> In alt.language.latin message <acglir...@mid.individual.net>, Wed,
>> 26 Sep 2012 16:34:23, Johannes Patruus <inv...@invalid.invalid> posted:
>>
>>>
>>> It's "distantia" here -
>>> http://books.google.co.uk/books?id=CVejrSJ2Q18C&pg=PA252
>>>
>>> Also, "id quo" in the first para should apparently be "id quod"
>>
>> Agreed.
>>
>> Page 246 of that reference is apparently part of an Abstract, the rest
>> of which I have found. The whole Abstract is now transcribed, but not
>> properly checked, in <http://www.merlyn.demon.co.uk/euler304.htm>.
>
>
> A generally much better rendition of the whole is in (scan of book)
>
> <http://archive.org/stream/novicommentariac10impe">
>
> Novi commentarii Academiae scientiarum imperialis petropolitanae, Tom.
> X., pro Anno MDCCLXIV (1766)
> E.304 : Abstract, pp.66-67, #page/n71; Index entry, #page/n75; Article,
> p.544-558, #page/544; Figure, #page/n677, upper.
>
> With a single mouse-click, the whole book can be heard, after a fashion.
>
>
> BTW : the original contains "desudasse", once in the Abstract and once
> in the Article. Google Translate disliked it, but liked "de sudasse" as
> meaning "sweated out", which fits. Comment?
>

desudasse is the preterite infinitive. de sudasse is nothing. de_ (de
space) is a preposition and needs to be linked with a substantive (I
assume here that sudasse is not an indeclinable verbal like "in esse").
Since Google Translate is only a (clunky) machine, it can't like or
dislike anything. Its algorithm is essentially aleatic. It takes the
mean of a set of ordered pairs of originals (ocr'ed and maybe edited)
and legacy versions (ocr'ed and maybe edited).


Eduardus

[Dr J R Stockton]

In alt.language.latin message <9XsQ8Rcv...@invalid.uk.co.demon.merl
yn.invalid>, Fri, 28 Sep 2012 23:29:03, Dr J R Stockton <reply1239@merly
n.demon.co.uk.invalid> posted:

>BTW : the original contains "desudasse", once in the Abstract and once
>in the Article. Google Translate disliked it, but liked "de sudasse" as
>meaning "sweated out", which fits. Comment?

Reply for both follow-ups : Thanks; I'll take it as "sweated out" for
the time being. Yes, I know Google Translate is often bad, especially
for less popular languages; for example (English to French) it
considered "May" to be a month rather than meaning something like
"perhaps" or "it is hoped" (or vice versa). May it improve; I've
already in this work alone noticed that it offers different translations
on different days for the same text.

I've added those links to the References of my page, where they will be
more useful. From what I recall, Lewis & Short is about 25 times bigger
than the Collins dictionary that I have, albeit with thicker paper.

--

[Dr J R Stockton]

In alt.language.latin message <k3v9fb$hv6$1...@dont-email.me>, Wed, 26 Sep
2012 17:10:01, Ed Cryer <e...@somewhere.in.the.uk> posted:

Having seen the discussion, and observing that to anyone with a general
knowledge of the topic the meaning of the English above will be
sufficiently clear, I've inserted said English virtually /verbatim/.


This sentence ends Section 3 :

Imbecillitati nostrae sapientissimus creator consuluisse videtur, quod
nulla corpora in coelo ita collacauerit, ut eorum motus, neque ad legem
planetarum principalium, neque satellitum, referri posset.

I've found nothing to say what "collacauerit" means (Google finds only
two other uses), but something like "co-located" might fit.


The Summary (recently found) contains several "Cel.Auctor", which I take
to mean "Celebrated Author", and to imply that the summary is by another
hand. It also has "celeberr." (celeberissimus?).


Of the main text, Sections 1 & 10 are now properly translated, 2 & 4 are
only in raw Google Translate, and about 50% of Section 3 has been
translated by me. Sections 5-9, 11-17 have also been translated by me,
numbered piecewise. My translations are in Column 4, grey background.
Some are probably good; others are undoubtedly bad.


It seems now best, for a change, to work on the amendment and acceptance
of those later portions. The very simplest I've accepted directly, but
feel free to say otherwise. Just post the acceptance or (more likely)
improvement here, with its number from Column 2. But by all means work
on other sections if you prefer.


<http://www.merlyn.demon.co.uk/euler304.htm> is the work so far, and, in
its References section, "NOW RECOMMENDED" marks the best primary source
to, if needed, use.

[Johannes Patruus]

On 30/09/2012 22:01, Dr J R Stockton wrote:

> This sentence ends Section 3 :
>
> Imbecillitati nostrae sapientissimus creator consuluisse videtur, quod
> nulla corpora in coelo ita collacauerit, ut eorum motus, neque ad legem
> planetarum principalium, neque satellitum, referri posset.
>
> I've found nothing to say what "collacauerit" means (Google finds only
> two other uses), but something like "co-located" might fit.
>
>
> The Summary (recently found) contains several "Cel.Auctor", which I take
> to mean "Celebrated Author", and to imply that the summary is by another
> hand. It also has "celeberr." (celeberissimus?).
>
>

> Of the main text, Sections 1& 10 are now properly translated, 2& 4 are

> only in raw Google Translate, and about 50% of Section 3 has been
> translated by me. Sections 5-9, 11-17 have also been translated by me,
> numbered piecewise. My translations are in Column 4, grey background.
> Some are probably good; others are undoubtedly bad.
>
>
> It seems now best, for a change, to work on the amendment and acceptance
> of those later portions. The very simplest I've accepted directly, but
> feel free to say otherwise. Just post the acceptance or (more likely)
> improvement here, with its number from Column 2. But by all means work
> on other sections if you prefer.
>
>
> <http://www.merlyn.demon.co.uk/euler304.htm> is the work so far, and, in
> its References section, "NOW RECOMMENDED" marks the best primary source
> to, if needed, use.

Quick reply to one point before I have to go out -

"collacauerit" should be "collocaverit" (from the verb "colloco"). I found
a Google "snippet view" to confirm this, but not being able to see the
complete original is an impediment.

Patruus

[Johannes Patruus]

On 30/09/2012 22:01, Dr J R Stockton wrote:

> This sentence ends Section 3 :
>
> Imbecillitati nostrae sapientissimus creator consuluisse videtur, quod
> nulla corpora in coelo ita collacauerit, ut eorum motus, neque ad legem
> planetarum principalium, neque satellitum, referri posset.

"The all-wise Creator seems to have had regard for our weakness, for there
are no bodies in the heavens which He has placed in such a manner that
their motion could be referred[1] neither to the law of the principal
planets nor of satellites."

[1] or, perhaps, "related", ultra-literally "carried back".

> I've found nothing to say what "collacauerit" means (Google finds only
> two other uses), but something like "co-located" might fit.

[Repeated from earlier post:] "collacauerit" should be "collocaverit"

(from the verb "colloco"). I found a Google "snippet view" to confirm
this, but not being able to see the complete original is an impediment.

> The Summary (recently found) contains several "Cel.Auctor", which I take
> to mean "Celebrated Author", and to imply that the summary is by another
> hand. It also has "celeberr." (celeberissimus?).

Rather, "celeberrimus" -
http://en.wiktionary.org/wiki/celeberrimus

"In Latin, the superlative degree is often a mere elative. This usage is
in keeping with the Roman character which was somewhat inclined to
rhetorical exaggeration." (James A Kleist, Aids to Latin Composition, p.30)

I would take "Cel." to mean the same. Can render as renowned,
distinguished, celebrated, famous, etc.

> Of the main text, Sections 1& 10 are now properly translated, 2& 4 are

> only in raw Google Translate, and about 50% of Section 3 has been
> translated by me. Sections 5-9, 11-17 have also been translated by me,
> numbered piecewise. My translations are in Column 4, grey background.
> Some are probably good; others are undoubtedly bad.
>
>
> It seems now best, for a change, to work on the amendment and acceptance
> of those later portions. The very simplest I've accepted directly, but
> feel free to say otherwise. Just post the acceptance or (more likely)
> improvement here, with its number from Column 2. But by all means work
> on other sections if you prefer.

Speaking for myself, I have, alas, neither the time nor the energy nor the
skill to engage in systematic translation of a text fraught with so many
difficulties (including transcriptional).

> <http://www.merlyn.demon.co.uk/euler304.htm> is the work so far, and, in
> its References section, "NOW RECOMMENDED" marks the best primary source
> to, if needed, use.

Patruus

[Dr J R Stockton]

In alt.language.latin message <acsv2p...@mid.individual.net>, Mon, 1
Oct 2012 08:29:37, Johannes Patruus <inv...@invalid.invalid> posted:

>On 30/09/2012 22:01, Dr J R Stockton wrote:

>> I've found nothing to say what "collacauerit" means (Google finds only
>> two other uses), but something like "co-located" might fit.

>Quick reply to one point before I have to go out -
>
>"collacauerit" should be "collocaverit" (from the verb "colloco"). I
>found a Google "snippet view" to confirm this, but not being able to
>see the complete original is an impediment.

Obviously not one of the several alternatives that I have offered to
Google Translate, which gives "placed" for it. So "located" would do,
but not "co-located".

Thanks.

--

[Dr J R Stockton]

In alt.language.latin message <actpqf...@mid.individual.net>, Mon, 1
Oct 2012 16:05:51, Johannes Patruus <inv...@invalid.invalid> posted:

>On 30/09/2012 22:01, Dr J R Stockton wrote:
>
>> This sentence ends Section 3 :
>>
>> Imbecillitati nostrae sapientissimus creator consuluisse videtur, quod
>> nulla corpora in coelo ita collacauerit, ut eorum motus, neque ad legem
>> planetarum principalium, neque satellitum, referri posset.
>
>"The all-wise Creator seems to have had regard for our weakness, for
>there are no bodies in the heavens which He has placed in such a manner
>that their motion could be referred[1] neither to the law of the
>principal planets nor of satellites."
>
>[1] or, perhaps, "related", ultra-literally "carried back".

It makes the same sense either way. Inserted.

>> I've found nothing to say what "collacauerit" means (Google finds only
>> two other uses), but something like "co-located" might fit.
>
>[Repeated from earlier post:] "collacauerit" should be "collocaverit"
>(from the verb "colloco"). I found a Google "snippet view" to confirm
>this, but not being able to see the complete original is an impediment.

A better copy, well-printed, slightly faded, well-scanned, complete, is
at <http://archive.org/stream/novicommentariac10impe>

Novi commentarii Academiae scientiarum imperialis petropolitanae,

Tom. X., pro Anno MDCCLXIV</a> (1766) -
Summary, pp.66-67, #page/n71;

Index entry, #page/n75;
Article, p.544-558, #page/544;
Figure, #page/n677, upper.

I wish I had seen it in the first place.

The word as shown there is clearly "collacauerit", as in another scan of
the same book. Google Books, which has an edited printing, refuses to
show that page. But your interpretation is manifestly correct.

>> The Summary (recently found) contains several "Cel.Auctor", which I take
>> to mean "Celebrated Author", and to imply that the summary is by another
>> hand. It also has "celeberr." (celeberissimus?).
>
>Rather, "celeberrimus" -
> http://en.wiktionary.org/wiki/celeberrimus
>
>"In Latin, the superlative degree is often a mere elative. This usage
>is in keeping with the Roman character which was somewhat inclined to
>rhetorical exaggeration." (James A Kleist, Aids to Latin Composition,
>p.30)
>
>I would take "Cel." to mean the same. Can render as renowned,
>distinguished, celebrated, famous, etc.

Noted.

>> Of the main text, Sections 1& 10 are now properly translated, 2& 4 are
>> only in raw Google Translate, and about 50% of Section 3 has been
>> translated by me. Sections 5-9, 11-17 have also been translated by me,
>> numbered piecewise. My translations are in Column 4, grey background.
>> Some are probably good; others are undoubtedly bad.
>>
>>
>> It seems now best, for a change, to work on the amendment and acceptance
>> of those later portions. The very simplest I've accepted directly, but
>> feel free to say otherwise. Just post the acceptance or (more likely)
>> improvement here, with its number from Column 2. But by all means work
>> on other sections if you prefer.
>
>Speaking for myself, I have, alas, neither the time nor the energy nor
>the skill to engage in systematic translation of a text fraught with so
>many difficulties (including transcriptional).

My thanks for what you have done - perhaps others will be able to do
more. There's not a great deal left for which I have nothing either
slightly or greatly better than the raw Google translation.

>> <http://www.merlyn.demon.co.uk/euler304.htm> is the work so far, and, in
>> its References section, "NOW RECOMMENDED" marks the best primary source
>> to, if needed, use.

As above.

[Dr J R Stockton]

In alt.language.latin message <uwakVAHz...@invalid.uk.co.demon.merl
yn.invalid>, Mon, 24 Sep 2012 12:01:07, Dr J R Stockton <reply1239@merly
n.demon.co.uk.invalid> posted:

>I happened to be reading, before breakfast today, Volume 1 (Books I &
>II) of "Euclid / the thirteen books of The Elements", 2nd edition, by

>Sir Thomas L Heath, pub. Dover, supplier Oxfam, and reached the last
>paragraph of "Additional Axioms", in Book 1 : Notes and Definitions,
>etc., page 234.
>
>Heath quotes Archimedes : "... they have proved that circles have to one
>another the duplicate ratio of their diameters, that spheres have to one

>another the triplicate ratio of their diameters, and so on.". So
>Euler's usage has sufficiently illustrious precedent.

>
>If anyone sees Vols 2 or 3 of Heath in their local Oxfam, please ask for
>one copy to be moved to the New Malden branch.

I wish firstly to acknowledge the generosity of a lurker here, who has
given me Volumes 2 & 3, same edition and publisher.


And secondly to say that <http://www.merlyn.demon.co.uk/euler304.htm> is
now in a nominally complete state. The mathematical parts have my own
translation, and the discursive parts are partly as given here and
partly as raw Google Translate. It all makes sufficient sense for
anyone interested in the subject to be able to understand what Euler was
doing.

I shall of course install any corrections or improvements received.

--

[Dr J R Stockton]

In alt.language.latin message <Ud4Nf5V1...@invalid.uk.co.demon.merl
yn.invalid>, Mon, 8 Oct 2012 23:30:13, Dr J R Stockton <reply1241@merlyn
.demon.co.uk.invalid> posted:

>And secondly to say that <http://www.merlyn.demon.co.uk/euler304.htm> is
>now in a nominally complete state. The mathematical parts have my own
>translation, and the discursive parts are partly as given here and
>partly as raw Google Translate. It all makes sufficient sense for
>anyone interested in the subject to be able to understand what Euler was
>doing.

You've now all had over a month's rest from
<http://www.merlyn.demon.co.uk/euler304.htm>. There are a few small
parts of the Latin, away from the main maths, for which I don't have a
fully meaningful translation.

The authoritative legible source for the Latin is
<http://archive.org/stream/novicommentariac10impe#page/n5/mode/2up>,

Novi commentarii Academiae scientiarum imperialis petropolitanae, Tom.

X., pro Anno MDCCLXIV (1766) -

Summary, pp.66-67, #page/n71; Index entry, #page/n75; Article,
p.544-558, #page/544; Figure, #page/n677, upper.

The Latin is (on pages 545-546, rechecked)

"Tantopere certe ab omnibus motibus in coelo observatis discreparet, ut
vix intelligi possit, quemadmodem saltem ideam motus medii constitui
conveniat."

for which I have

"Certainly all the motions observed in the heavens differed so much,
that they could scarcely be understood, as had at least
the idea of the motion of the medium becoming established."

of which the first two lines seem about right, but the third does not.

Any suggestions?

--
(c) John Stockton, nr London, UK. E-mail, see Home Page. Turnpike v6.05.

[Johannes Patruus]

On 13/11/2012 18:32, Dr J R Stockton wrote:
> In alt.language.latin message<Ud4Nf5V1...@invalid.uk.co.demon.merl
> yn.invalid>, Mon, 8 Oct 2012 23:30:13, Dr J R Stockton<reply1241@merlyn
> .demon.co.uk.invalid> posted:
>
>> And secondly to say that<http://www.merlyn.demon.co.uk/euler304.htm> is
>> now in a nominally complete state. The mathematical parts have my own
>> translation, and the discursive parts are partly as given here and
>> partly as raw Google Translate. It all makes sufficient sense for
>> anyone interested in the subject to be able to understand what Euler was
>> doing.
>
>
> You've now all had over a month's rest from
> <http://www.merlyn.demon.co.uk/euler304.htm>. There are a few small
> parts of the Latin, away from the main maths, for which I don't have a
> fully meaningful translation.
>
> The authoritative legible source for the Latin is
> <http://archive.org/stream/novicommentariac10impe#page/n5/mode/2up>,
> Novi commentarii Academiae scientiarum imperialis petropolitanae, Tom.
> X., pro Anno MDCCLXIV (1766) -
> Summary, pp.66-67, #page/n71; Index entry, #page/n75; Article,
> p.544-558, #page/544; Figure, #page/n677, upper.
>
>
> The Latin is (on pages 545-546, rechecked)
>
> "Tantopere certe ab omnibus motibus in coelo observatis discreparet, ut
> vix intelligi possit, quemadmodem saltem ideam motus medii constitui
> conveniat."

For "quemadmodem" read "quemadmodum".

> for which I have
>
> "Certainly all the motions observed in the heavens differed so much,
> that they could scarcely be understood, as had at least
> the idea of the motion of the medium becoming established."
>
> of which the first two lines seem about right, but the third does not.
>
> Any suggestions?

From the text immediately preceding the above, it would appear that the
subject of the verb "discreparet" is the motion of the Moon. Moreover the
subjunctive mood of this verb suggests that it is an extension of the
apodosis of the preceding conditional sentence. Thus -

"It [i.e. the Moon's motion] would certainly[*] differ so much from all
the motions observed in the heavens that it is scarcely intelligible how .
. ."

[*] Perhaps better: "At any rate, it would differ . . ."

The indirect question introduced by 'quemadmodum' (how, in what way)
defeats me, at least for the moment.

Patruus

[Ed Cryer]

How about "just how the very notion of 'middle motion' can be established".
I don't know what "middle motion" is; but am hopeful that someone might.

Ed

[Ed Cryer]

Ed Cryer wrote:

>
> quemadmodem saltem ideam motus medii constitui conveniat."
> How about "just how the very notion of 'middle motion' can be
established".
> I don't know what "middle motion" is; but am hopeful that someone might.
>
> Ed
>

Whatever it is or was, "motus medius" was a used term.
http://tinyurl.com/d494j3p

Euler himself wrote something with the title;
Meditationes in quaestionem utrum motus medius planetarum semper maneat
aeque velox, an successu temporis quampiam mutationem patiatur? &
quaenam sit ejus causa?
(Considerations of the question whether the "middle motion" of the
planets remains always just the same speed, or whether it changes at all
with time, & what be the cause of the latter.)

It couldn't be "mean" or "average", could it?

Ed

[Evertjan.]

Ed Cryer wrote on 14 nov 2012 in alt.language.latin:

> Whatever it is or was, "motus medius" was a used term.

Perhaps movement of the middle sphere?

If not an explanation of Rubic's cube,
it could be the motion the sphere of the sun,
see <http://tinyurl.com/d4y9b52>

Medieval astronomers and philosophers developed diverse theories about the
causes of the celestial spheres' motions.
[../..]
in [those] celestial models the stars and planets are carried around by
being embedded in rotating spheres made of an aetherial transparent fifth
element (quintessence)
[..]
Ancient and medieval thinkers [..] considered the celestial orbs to be
thick spheres of rarefied matter nested one within the other, each one in
complete contact with the sphere above it and the sphere below.
[..]
Each of these concentric spheres is moved by its own god � an unchanging
divine unmoved mover, and who moves its sphere simply by virtue of being
loved by it.

<http://en.wikipedia.org/wiki/Celestial_spheres>

--
Evertjan.
The Netherlands.
(Please change the x'es to dots in my emailaddress)

[Ed Cryer]

Got it, I think. "Centrifugal motion".
It's the speed of a planet's rotation on its axis as it moves through space.

Ed

[Ed Cryer]

Homines enim sunt hac lege generati, qui tuerentur
illum globum, quem in hoc templo medium vides,
quae terra dicitur, iisque animus datus est ex illis
sempiternis ignibus, quae sidera et stellas vocatis,
quae globosae et rotundae, divinis animatae mentibus,
circulos suos orbesque conficiunt celeritate mirabili.
(Cicero; De Republica)
For men were created under this rule, that they should maintain that
globe which you see in the middle of this temple, known as Earth, and a
soul is given them from those eternal fires which you call stars and
heavenly bodies, and which are round and spherical, brought to life by
divine minds, and complete their orbits and circles with wondrous speed.

Cool! Like a hippie's paradise; "We are star-dust, we are golden; and
we've got to get ourselves back to the Garden."

Or;
"We are a way for the universe to know itself. Some part of our being
knows this is where we came from. We long to return. And we can, because
the cosmos is also within us. We're made of star stuff,"
(Carl Sagan)


Ed

[John W Kennedy]

"Centrifugal motion" only occurs in objects that are exploding. And
planets in the medieval universe didn't rotate.

--
John W Kennedy
"Compact is becoming contract,
Man only earns and pays."
-- Charles Williams. "Bors to Elayne: On the King's Coins"

[Ed Cryer]

Does the Enlightenment count as "medieval"?

centrifugal force n
(Physics / General Physics) a fictitious force that can be thought of as
acting outwards on any body that rotates or moves along a curved path
(Collins English Dictionary – Complete and Unabridged © Harper Collins
Publishers 1991, 1994, 1998, 2000, 2003)


Hicetas Syracosius, ut ait Theophrastus, caelum solem lunam
stellas, supera denique omnia stare censet neque praeter terram rem
ullam in mundo moueri, quae cum circum
axem se summa celeritate conuertat et torqueat, eadem effici omnia, quae
si stante terra caelum moueretur.
(Cicero)
"Hicetas the Syracusan, as Theophrastos says, believes that the sky,
sun, moon,
stars, and in fact all the heavenly bodies stand still, and that nothing
at all moves in the universe except the earth;
and that because it turns and twists with great speed about its axis,
all the same phenomena are produced as if the
sky was in motion and the earth standing still."

That gives us "circum axem converti" for "revolves on its axis".

Ed

[Ed Cryer]

Ubi haec aequatio additur vel subducitur medio motui Solis debet eius
pars decima e contra subduci vel addi medio motui Lunae. Nam medius
motus Lunae non est uniformis sed per vices tardescit et acceleratur
propterea quod orbis Lunae dilatur in perigaeo Solis et contrahitur in
eius Apogaeo.
(Isaac Newton)
When this equation is added to or subtracted from the "medius motus" of
the Sun a tenth part of it should be likewise added to or subtracted
from the "medius motus" of the Moon. For the Moon's "medius motus" isn't
uniform but alternately slows and accelerates because the Moon's orb
dilates in perigee to the Sun and contracts in apogee.


Ed

[John W Kennedy]

Sorry -- I had to search back to September to discover that this is
Enlightenment.

>
> centrifugal force n
> (Physics / General Physics) a fictitious force that can be thought of
> as acting outwards on any body that rotates or moves along a curved path
> (Collins English Dictionary – Complete and Unabridged © Harper Collins
> Publishers 1991, 1994, 1998, 2000, 2003)
>
>
> Hicetas Syracosius, ut ait Theophrastus, caelum solem lunam
> stellas, supera denique omnia stare censet neque praeter terram rem
> ullam in mundo moueri, quae cum circum
> axem se summa celeritate conuertat et torqueat, eadem effici omnia,
> quae si stante terra caelum moueretur.
> (Cicero)
> "Hicetas the Syracusan, as Theophrastos says, believes that the sky,
> sun, moon,
> stars, and in fact all the heavenly bodies stand still, and that
> nothing at all moves in the universe except the earth;
> and that because it turns and twists with great speed about its axis,
> all the same phenomena are produced as if the
> sky was in motion and the earth standing still."
>
> That gives us "circum axem converti" for "revolves on its axis".

An eccentric view. (See what I did there?)

Anyway, none of that gives "centrifugal motion", which more or less
/means/ "explosion" -- "running away from the center".

--
John W Kennedy
"You can, if you wish, class all science-fiction together; but it is
about as perceptive as classing the works of Ballantyne, Conrad and W.
W. Jacobs together as the 'sea-story' and then criticizing _that_."
-- C. S. Lewis. "An Experiment in Criticism"

[John W Kennedy]

Now /that/ smells like "average".

--
John W Kennedy
"I want everybody to be smart. As smart as they can be. A world of
ignorant people is too dangerous to live in."
-- Garson Kanin. "Born Yesterday"

[Ed Cryer]

http://tinyurl.com/c4c67lf
This one translates it as "mean motion".
Is that what we'd call "average speed".

Ed

[Ed Cryer]

http://www.youtube.com/watch?v=9cjzdAdcXsA
That centrifuge doesn't "explode". It revolves around a fixed central point.

Ed

[John W Kennedy]

You keep confusing "centrifugal force", which is a real term in physics
(albeit often frowned upon), with "centrifugal motion", which, as far
as I know, is a phrase that you just created for this thread as an
alias for "rotation", and which makes no etymological sense.


--
John W Kennedy
"Those in the seat of power oft forget their failings and seek only the
obeisance of others! Thus is bad government born! Hold in your heart
that you and the people are one, human beings all, and good government
shall arise of its own accord! Such is the path of virtue!"
-- Kazuo Koike. "Lone Wolf and Cub: Thirteen Strings" (tr. Dana Lewis)

[John W Kennedy]

In this case, roughly, yes.


--
John W Kennedy
"Sweet, was Christ crucified to create this chat?"
-- Charles Williams. "Judgement at Chelmsford"

[Dr J R Stockton]

In alt.language.latin message <Mty1gGVb...@invalid.uk.co.demon.merl
yn.invalid>, Tue, 13 Nov 2012 18:32:59, Dr J R Stockton <reply1246@merly
n.demon.co.uk.invalid> posted:

This is a general answer to six replies fetched before midnight
yesterday.

"quemadmodem" : I checked that part repeatedly before posting, and it
always seemed in both sources to be ...modem. But now it is ...modum.
Thanks : that shows the advantage of knowing the language that one is
reading.

"motus medii" : After seeing a suggestion implying that "medii" is not
"medium" as a substance but is "middle" : "mean motion" is an
established relevant term. The Earth's speed and angular speed round
the Sun varies through the year, as the orbit is elliptical; the angular
"mean motion" (ignoring details) is 360 degrees per year.

That agrees with Ed's next post.

By Euler's time, the idea of celestial spheres was dead.

Nothing to do here with rotation of a planet about its axis, which in
c.18 terms was constant (and in this case is irrelevant). But
ingenious.



I now have

", quemadmodum saltem ideam motus medii constitui conveniat." ->
", at least the idea of the mean motion became established." -- which is
not good English, but makes plausible applicable sense.

It will suffice.

Thanks to all.

--

[Ed Cryer]

Even better than old Hicetas was Aristarchos of Samos, a contemporary of
Archimedes. He developed a full heliocentric model, with earth and other
planets moving;
http://en.wikipedia.org/wiki/Aristarchus_of_Samos

Why didn't it catch on? Aristotle! Ptolemy followed Aristotle's model.
In fact the very name of "Aristotle" was almost like a stamp of truth
for ages and ages. If Aristotle had said it was so, then so it was.
The Enlightenment was to a large extent the overthrowing of Aristotle's
views; and the method used was empirical science.

Ed

[John W Kennedy]

They both favored geocentrism, but neither invented it, and Ptolemy's
system is significantly different from Aristotle's.

> In fact the very name of "Aristotle" was almost like a stamp of truth
> for ages and ages. If Aristotle had said it was so, then so it was.

No it wasn't. In particular, in the West, Aristotle was almost unknown
from roughly the fall of Rome to the 13th century.

--
John W Kennedy
"The poor have sometimes objected to being governed badly; the rich
have always objected to being governed at all."
-- G. K. Chesterton. "The Man Who Was Thursday"

[John Briggs]

>> Even better than old Hicetas was Aristarchos of Samos, a contemporary
>> of Archimedes. He developed a full heliocentric model, with earth and
>> other planets moving;
>> http://en.wikipedia.org/wiki/Aristarchus_of_Samos
>>
>> Why didn't it catch on? Aristotle! Ptolemy followed Aristotle's model.
>
> They both favored geocentrism, but neither invented it, and Ptolemy's
> system is significantly different from Aristotle's.
>
>> In fact the very name of "Aristotle" was almost like a stamp of truth
>> for ages and ages. If Aristotle had said it was so, then so it was.
>
> No it wasn't. In particular, in the West, Aristotle was almost unknown
> from roughly the fall of Rome to the 13th century.

Where did transubstantiation come from then?
--
John Briggs

[Dr J R Stockton]

In alt.language.latin message <50a46b2e$0$1212$607e...@cv.net>, Wed, 14
Nov 2012 23:10:22, John W Kennedy <jwk...@attglobal.net> posted:

>"Centrifugal motion" only occurs in objects that are exploding. And
>planets in the medieval universe didn't rotate.

Euler was not mediaeval - he was not much older than the USA.

--

[Dr J R Stockton]

In alt.language.latin message <k8397e$80n$1...@dont-email.me>, Thu, 15 Nov
2012 17:36:05, Ed Cryer <e...@somewhere.in.the.uk> posted:

>
>http://tinyurl.com/c4c67lf
>This one translates it as "mean motion".
>Is that what we'd call "average speed".

Not quite; in our context, motion is a rate of change in angular
position on the celestial sphere, whereas speed is a rate of change of
position in space. The units are incommensurate.

[Dr J R Stockton]

In alt.language.latin message <50a57308$0$9810$607e...@cv.net>, Thu, 15
Nov 2012 17:56:31, John W Kennedy <jwk...@attglobal.net> posted:

>You keep confusing "centrifugal force", which is a real term in physics
>(albeit often frowned upon),

In your country maybe; in Europe we physicists know better, and leave it
to the engineers. We do acknowledge centripetal force (from petere, of
course); where it exists, it is real.

> with "centrifugal motion", which, as far as I know, is a phrase that
>you just created for this thread as an alias for "rotation", and which
>makes no etymological sense.

The true meaning of "centrifugal motion" means like what the outside of
a hand grenade does a little while after the pin is pulled. Or what we
are all doing as a consequence of the Big Bang, except that in that case
there was and is no centre, since at the Bang everywhere was at the same
place. Or roughly so; theories are numerous and volatile.


This thread is about a work by Euler which in part involves what are now
known as Lagrange Points L1 & L2 (not L3, as far as I can see). Popular
expositions use the fictitious centrifugal force. Contrast them with
the methods used by Lagrange, myself, and European professionals - which
are much nicer.

--
(c) John Stockton, near London. Mail ?.?.Stoc...@physics.org
Web <http://www.merlyn.demon.co.uk/> - FAQish topics, acronyms, and links.

[Ed Cryer]

The Catholic Church could find people like Giordano Bruno and Galileo
guilty of heresy because Thomas Aquinas had fused Aristotelianism with
Christianity, and their teachings were refuting the cosmology and
physics involved.

Ed

[John W Kennedy]

The 13th century.

--
John W Kennedy
"Never try to take over the international economy based on a radical
feminist agenda if you're not sure your leader isn't a transvestite."
-- David Misch: "She-Spies", "While You Were Out"

[John W Kennedy]

A) You apparently do not understand what is meant by "the 13th century".

B) Bruno's condemnation had nothing to do with astronomy (and, by the
way, his astronomical notions, taken as a whole, were as loopy as
Scientology). He was condemned for his flat-out denial of Christianity.

C) Copernicanism had been allowed as a theory all along, for about a
century before Galileo, who was found guilty, not of teaching
Copernicanism, but of implying that anyone who didn't accept
Copernicanism (such as the Pope) was a fool. And the RCC's main
arguments against Copernicanism were based on passages in the Bible.
Essentially, Galileo was found guilty of being a dick.

--
John W Kennedy
"The bright critics assembled in this volume will doubtless show, in
their sophisticated and ingenious new ways, that, just as /Pooh/ is
suffused with humanism, our humanism itself, at this late date, has
become full of /Pooh./"
-- Frederick Crews. "Postmodern Pooh", Preface

[John W Kennedy]

On 2012-11-16 19:33:32 +0000, Dr J R Stockton said:

> In alt.language.latin message <50a57308$0$9810$607e...@cv.net>, Thu, 15
> Nov 2012 17:56:31, John W Kennedy <jwk...@attglobal.net> posted:
>
>> You keep confusing "centrifugal force", which is a real term in physics
>> (albeit often frowned upon),
>
> In your country maybe; in Europe we physicists know better, and leave it
> to the engineers. We do acknowledge centripetal force (from petere, of
> course); where it exists, it is real.

And centrifugal force is real in a rotating frame of reference. But,
indeed, I never said that it was not a fictitious force, only that it
is a phrase employed in the discussion of physics, to deny which is
absurd; you might as well say that "unicorn" is not an English word.
The corrolary to "The map is not the territory" is "The territory is
not the map."

>> with "centrifugal motion", which, as far as I know, is a phrase that
>> you just created for this thread as an alias for "rotation", and which
>> makes no etymological sense.
>
> The true meaning of "centrifugal motion" means like what the outside of
> a hand grenade does a little while after the pin is pulled.

That is exactly what I said.

--
John W Kennedy
Having switched to a Mac in disgust at Microsoft's combination of
incompetence and criminality.

[Ed Cryer]

One man's dick is another's hero. It depends on your point of view; the
power structure, belief and value system you've bought into.
It's easy to make someone look a dick. Depower them, make them look
ridiculous. I've got no doubt that in the amphitheatres of the Roman
Empire the Christian martyrs looked real dicks; "Look at them there
dicks - all they had to do was bow to the emperor's statue and renounce
their faith".

I'll bet Socrates came across as a real dick at his trial. And when he
moved into disrespectful defiance and suggested that his punishment
should be to be housed and fed at public expense, well, I bet he brought
the house down. What a dick!"
And as for Jesus dragging his cross along the Via Dolorosa, well, a bit
of a dick to quite a few at the time.

The Catholic Church's Index Librorum Prohibitorum contained many, many
philosophical works; and many that are now set books for English
undergrad philosophy students. Amongst them were; Jean-Paul Sartre,
Simone de Beauvoir, Voltaire, Denis Diderot, Victor Hugo, Jean-Jacques
Rousseau, André Gide, Immanuel Kant, David Hume, René Descartes, Francis
Bacon, John Milton, John Locke, Galileo Galilei, Blaise Pascal and
Johannes Kepler.


Ed

[John W Kennedy]

Nice evasion.

--
John W Kennedy
A proud member of the reality-based community.

[John Briggs]

No, it's quite a bit earlier than that. The term itself dates from the
end of the 11th century, and it becomes more widespread by the end of
the 12th. It is *confirmed* at Lateran IV in 1215. The concept is
unmistakeably Aristotlean - but what is an Aristotlean term doing
knocking around in the 11th century?
--
John Briggs

[Evertjan.]

John W Kennedy wrote on 16 nov 2012 in alt.language.latin:

> No it wasn't. In particular, in the West, Aristotle was almost unknown
> from roughly the fall of Rome to the 13th century.

This depends on your definition of "the west",
surely not being Ireland or the "American west" here?

The Rambam [Mosjeh ben Maimon, Maimonides, Cordoba 1135-Cairo 1204]
was a self-declared fan of Aristotle.

See book two of the Rambam's "Moreh Nebuchim" [original in Arabic].
<http://en.wikipedia.org/wiki/The_Guide_for_the_Perplexed>

--
Evertjan.
The Netherlands.
(Please change the x'es to dots in my emailaddress)

[Ed Cryer]

Evertjan. wrote:
> John W Kennedy wrote on 16 nov 2012 in alt.language.latin:
>
>> No it wasn't. In particular, in the West, Aristotle was almost unknown
>> from roughly the fall of Rome to the 13th century.
>
> This depends on your definition of "the west",
> surely not being Ireland or the "American west" here?
>
> The Rambam [Mosjeh ben Maimon, Maimonides, Cordoba 1135-Cairo 1204]
> was a self-declared fan of Aristotle.
>
> See book two of the Rambam's "Moreh Nebuchim" [original in Arabic].
> <http://en.wikipedia.org/wiki/The_Guide_for_the_Perplexed>
>

I think we have to thank the Islamic world for reintroducing Aristotle
to medieval European scholars. They first encountered him in Arabic
translations; and put those into Latin.

By Aquinas' time the phrase "ille philosophus" (the philosopher)
referred to Aristotle.

Ed

[Ed Cryer]

Cicero referred to Aristotle's style as "flumen orationis aureum fundens
Aristoteles" (a golden river of words).

Ed

[Evertjan.]

Ed Cryer wrote on 19 nov 2012 in alt.language.latin:

> I think we have to thank the Islamic world for reintroducing Aristotle
> to medieval European scholars. They first encountered him in Arabic
> translations; and put those into Latin.

An scientifically important part of medieval Europe being Islamic.

> By Aquinas' time the phrase "ille philosophus" (the philosopher)
> referred to Aristotle.

Nice.

[John W Kennedy]

I really don't know, as I cannot find enough solid information to build
on. Perhaps it was introduced in a Platonic form. One way or the other,
it is a well-established fact of history that the actual works of
Aristotle, with few exceptions, were unknown in the West at that time.
Wikipedia summarizes the matter under "Recovery of Aristotle", but
you'll find it in any general survey of medieval history, or in any
introduction to Thomas Aquinas, or, for that matter, Dante.

[John W Kennedy]

On 2012-11-19 07:43:39 +0000, Evertjan. said:

> John W Kennedy wrote on 16 nov 2012 in alt.language.latin:
>
>> No it wasn't. In particular, in the West, Aristotle was almost unknown
>> from roughly the fall of Rome to the 13th century.
>
> This depends on your definition of "the west",
> surely not being Ireland or the "American west" here?
>
> The Rambam [Mosjeh ben Maimon, Maimonides, Cordoba 1135-Cairo 1204]
> was a self-declared fan of Aristotle.
>
> See book two of the Rambam's "Moreh Nebuchim" [original in Arabic].
> <http://en.wikipedia.org/wiki/The_Guide_for_the_Perplexed>

At that time, Spain doesn't exactly count as "West". But it was indeed
from Spain, especially Averroes, that Aristotle reached England,
France, Germany, Italy, etc.

[Ed Cryer]

Evertjan. wrote:
> Ed Cryer wrote on 19 nov 2012 in alt.language.latin:
>
>> I think we have to thank the Islamic world for reintroducing Aristotle
>> to medieval European scholars. They first encountered him in Arabic
>> translations; and put those into Latin.
>
> An scientifically important part of medieval Europe being Islamic.
>
>> By Aquinas' time the phrase "ille philosophus" (the philosopher)
>> referred to Aristotle.
>
> Nice.
>

Yes, but strange to anyone who's actually read Aristotle's Greek. The
general opinion is that the books that have come down to us are not much
more than lecture notes, and that the ones Cicero read have now been lost.

I always like to compare the medieval Islamic world with Christendom.
The latter often comes out as prejudiced and bigoted by the comparison.
The lowest point occurred on November 27, 1095, when Pope Urban II
called upon all Christians in Europe to war against Muslims in order to
reclaim the Holy Land, with a cry of "Deus vult!"


Ed

[Ed Cryer]

The Last Supper is well covered in the NT; as are Jesus' words "this is
my body". Luke's version reads "Τοῦτό ἐστιν τὸ σῶμά μου" which is
undisputable in meaning.
Now, that raises a question to any thinking man. You don't need
Aristotelian ideas to come up with a word to describe it. And surely
that's what "transubstantio" does. It's rather like "the Word made
flesh". Some gateway from the ideal into the natural world.

Personally, to me it sounds more like Plato than Aristotle.

Ed

[Johannes Patruus]

On 19/11/2012 18:18, Ed Cryer wrote:

>[. . .]

>
> I always like to compare the medieval Islamic world with Christendom. The
> latter often comes out as prejudiced and bigoted by the comparison.
> The lowest point occurred on November 27, 1095, when Pope Urban II called
> upon all Christians in Europe to war against Muslims in order to reclaim
> the Holy Land, with a cry of "Deus vult!"

Among the Latin books I came upon yesterday at this site[1] is one
entitled "De Expugnatione Terrae Sanctae per Saladinum Libellus",
previewable at Amazon [2].

[1] http://www.arepo.biz/latin-non-fiction.php
[2] http://www.amazon.co.uk/dp/1449562957/

Patruus

[John Briggs]

Actually, those are interpolations into the Gospel accounts. (Nothing of
the sort happens in John, of course.) And taken from Paul's account in
Corinthians, of course - which is less definite ("Do this in remembrance
of me.")

> Now, that raises a question to any thinking man. You don't need
> Aristotelian ideas to come up with a word to describe it. And surely
> that's what "transubstantio" does. It's rather like "the Word made
> flesh". Some gateway from the ideal into the natural world.

No. "Transubstantio" has no meaning outside Aristotlean philosophy.

> Personally, to me it sounds more like Plato than Aristotle.

Does Plato use the word?
--
John Briggs

[Ed Cryer]

I guess the Greek equivalent of the word would be μετουσία.
Both Plato and Aristotle use the term.
For Plato it = participation in universal forms.
For Aristotle it = participation in the universal by the particular.

Since Aristotle's universals are mere categories that exist only in the
particular, but Plato's forms are real and exist in some higher realm, I
repeat that "transubstantiation" seems more Platonic than Aristotelian.

Plotinus (neo-Platonist philosopher) used the term a lot.

Ed

[John W Kennedy]

On 2012-11-19 18:18:23 +0000, Ed Cryer said:

> Evertjan. wrote:
>> Ed Cryer wrote on 19 nov 2012 in alt.language.latin:
>>
>>> I think we have to thank the Islamic world for reintroducing Aristotle
>>> to medieval European scholars. They first encountered him in Arabic
>>> translations; and put those into Latin.
>>
>> An scientifically important part of medieval Europe being Islamic.
>>
>>> By Aquinas' time the phrase "ille philosophus" (the philosopher)
>>> referred to Aristotle.
>>
>> Nice.
>>
>
> Yes, but strange to anyone who's actually read Aristotle's Greek. The
> general opinion is that the books that have come down to us are not
> much more than lecture notes, and that the ones Cicero read have now
> been lost.

Aristotle was far more pragmatic and comprehensive than most of the
Greek world; it should be no surprise that he rose on the 11th-13th
centuries like a new dawn. We have developed a habit of pointing at his
errors and comparing him to Newton. (Then, too, the age had known the
Neoplatonists better than Plato.) It's rather like the situation with
Lamarck; we laugh at him and laud Darwin, but it was Lamarck who
actually developed the notion of evolution as a major force in
biology.I always like to compare the medieval Islamic world with

Christendom. The latter often comes out as prejudiced and bigoted by
the comparison.

> The lowest point occurred on November 27, 1095, when Pope Urban II
> called upon all Christians in Europe to war against Muslims in order to
> reclaim the Holy Land, with a cry of "Deus vult!"

If you are suggesting that it was nothing more than Urban's whim --
well, there was more to it than that. There was very real provocation.

--
John W Kennedy
"Only an idiot fights a war on two fronts. Only the heir to the throne
of the kingdom of idiots would fight a war on twelve fronts"
-- J. Michael Straczynski. "Babylon 5", "Ceremonies of Light and Dark"

[John Briggs]

Let's stick to Latin. Is Substance used in any of the Latin versions of
Plato?
--
John Briggs

[Ed Cryer]

Nice evasion attempt!

It's all a question of green and greenness.
How do you know that thing is green?
It looks green, and Fred Fernackapan also says it's green. Yes it's green.
But how can you say that you "know"? What is the relationship between
green and greenness?
Well, greenness is a general term to cover all green particulars.
Where does the concept come from? Do we as individuals arrive at it from
grouping particulars; or is the concept innate?
We might call the former theory inductive reasoning, the latter
deductive. "Metousia" is the relationship that a particular has with its
class universal.
For Plato it was deductive; for Aristotle inductive.

Plato's theory of forms was famous in his day, and has been in western
philosophy ever since; not to mention western religions.

St Augustine expounds a neo-Platonist view at great extent. He probably
got it through Plotinus rather than directly from Plato. And St
Augustine wrote in Latin and became exceedingly influential in later
medieval times

Ed

[Ed Cryer]

Don't be misled by the "substance" part of "transubstantiation". The
Eastern Orthodox Church called it μετουσιωσις, and the ουσία bit means
"being" in Greek.
"Substance" had a tortured and laboured passage through antiquity and
medieval times. The Scholastics hammered away at it for centuries.
The problem was that neither Plato nor Aristotle believed in the atomic
theory. You'll also find that the scientific revolution really took off
when it became generally accepted as an explanatory hypothesis for
physics. Which has produced for us a very different meaning for the
word; almost synonymous with "matter".

Ed

[John Briggs]

"Substance" was used in this context before "transubstantiation".
Everyone involved in the development of the concept of
transubstantiation was writing in Latin (the Eastern Orthodox Church
weren't involved), but using a concept derived (somehow) from Aristotle.
--
John Briggs

[Ed Cryer]

Aristotle used two terms; οὐσία and ποιότητες. Cicero translated these
as "essentia" and "qualitates". But Aquinas calls them "substantia" and
"accidentia".
The history of philosophy tends to stick with Aquinas (substance and
accidents).
Just where the change to Aquinas' terminology occurred I can't discover.

Ed

[Ed Cryer]

Ed Cryer wrote:
> John Briggs wrote:.

>>
>> "Substance" was used in this context before "transubstantiation".
>> Everyone involved in the development of the concept of
>> transubstantiation was writing in Latin (the Eastern Orthodox Church
>> weren't involved), but using a concept derived (somehow) from Aristotle.
>
> Aristotle used two terms; οὐσία and ποιότητες. Cicero translated these
> as "essentia" and "qualitates". But Aquinas calls them "substantia" and
> "accidentia".
> The history of philosophy tends to stick with Aquinas (substance and
> accidents).
> Just where the change to Aquinas' terminology occurred I can't discover.
>
> Ed
>

I should have guessed; Augustine. He uses "substantia" in his
discussions of the Trinity of God.
http://www.findingaugustine.org/Record/58727

Ed

[Dr J R Stockton]

In alt.language.latin message <23SbmSOd...@invalid.uk.co.demon.merl
yn.invalid>, Thu, 15 Nov 2012 20:33:33, Dr J R Stockton <reply1246@merly
n.demon.co.uk.invalid> posted:

>
>Thanks to all.
>

You people seem to have enjoyed what came of my previous snippet. This
one is actually a single sentence, for which I divide what I have so far
into three unequal parts.

"Plurimum abest, ut hoc problema aggredi ausim, ut potius, frustra in eo
evolvendo desudasse, fateri cogar ; verum tamen casum observavi omnino
singularem, ac simplicitate memorabilem, quo Lunae eiusmodi motus
imprimi potuisset, ut perpetuo Soli, vel coniuncta, vel opposita,
apparitura fuisset, cuius calus consideratio, cum forte usu in hoc
difficillimo negotio non destituatur, haud displicitura videtur."

The first short part has a "translation" which needs improvement :

"The most is absent, to this problem I would venture to undertake,
rather, "

The second shorter part is weird :

"in vain 'sweated out' evolve in it, "

and the largest part mostly makes fairly good sense already :

"I am compelled to admit that, nevertheless, I have observed a case of
unique and memorable simplicity, that the Moon could have been given
such motion that it would appear perpetually either in conjunction or in
opposition to the Sun, which shrewd reflection, perhaps with the chance
to use this difficult task is not left, it seems, not disagreeable."


I've RE-checked the transcription. Conjunction and Opposition are
relevant technical terms (describing New Moon & Full Moon). That part
of the text is of considerable importance in relation to what I am
really interested in.

Source is
<http://archive.org/stream/novicommentariac10impe#page/546/mode/2up>,
pp. 546-7, the end of Section 4, nicely printed.

--
(c) John Stockton, nr London, UK. Mail via homepage. Turnpike v6.05 MIME.
Web <http://www.merlyn.demon.co.uk/> - FAQqish topics, acronyms and links;
Astro stuff via astron-1.htm, gravity0.htm ; quotings.htm, pascal.htm, etc.

[Ed Cryer]

I did enjoy wrestling with "motus medius". I still don't understand it
but it appears to have gone the way of "phlogiston" and "ether". The
history of science is littered with abandoned theories. Not that that's
a bad thing, since science itself works with theory-formulation. It's
the great men like Newton and Einstein who tie them all together, but
smaller men have contributed the working theories. "Calamity theory",
"continental drift" and the "Higgs boson" were all theories early on.

This Latin seems easier to me. I also like Euler's great enthusiasm for
leaping in to consider a special case. It's something that's not
peculiar to mathematicians; you'll find it in philosophers and
scientists. As I said above, it's abstract theorising that drives
science generally.

"Plurimum abest, ut hoc problema aggredi ausim, ut potius, frustra in eo
evolvendo desudasse, fateri cogar ; verum tamen casum observavi omnino
singularem, ac simplicitate memorabilem, quo Lunae eiusmodi motus
imprimi potuisset, ut perpetuo Soli, vel coniuncta, vel opposita,

apparitura fuisset, cuius casus consideratio, cum forte usu in hoc

difficillimo negotio non destituatur, haud displicitura videtur."

I've changed "calus" to "casus".

I am very far from daring to tackle this problem, nay rather I am forced
to confess that I've sweated in vain over trying to solve it. However I
have noticed a totally special case of memorable simplicity in which
motion of such kind could have been stamped on the moon that it would
have appeared in permanent either conjunction or opposition to the sun.
Consideration of this case won't, I think, be displeasing since perhaps
it is not without usefulness in this most difficult business.

Ed

[Dr J R Stockton]

In alt.language.latin message <k92k03$n3h$1...@dont-email.me>, Tue, 27 Nov
2012 14:50:11, Ed Cryer <e...@somewhere.in.the.uk> posted:

>I did enjoy wrestling with "motus medius". I still don't understand it
>but it appears to have gone the way of "phlogiston" and "ether".

No; it's still in active use, but Englished. It even has a page
<http://en.wikipedia.org/wiki/Mean_motion>. The Google translation of
the Finnish version of the page is moderately amusing. The term occurs
in the Google translation of <http://de.wikipedia.org/wiki/Satellitenbah
nelement>, too. And the Italian page is "Moto Medio".

See also in <http://en.wikipedia.org/wiki/Two-line_element_set> : ISS's
TLE includes an element explained as
8 53–63 Mean Motion [Revs per day] 15.72125391
which seems like a diurnal procession of nearly 16 dog-collars.

>This Latin seems easier to me. I also like Euler's great enthusiasm for
>leaping in to consider a special case. It's something that's not
>peculiar to mathematicians; you'll find it in philosophers and
>scientists. As I said above, it's abstract theorising that drives
>science generally.

Special cases are often easier than the general. See what I've written
about Lagrange's /Essai/ - by following his initial lead and immediately
going special case, nearly all of Chapter I is not needed to get the
special, interesting, answer. But in Chapter II, the sideline which
covers the part of interest to me, he twice followed the special with
its general. I expect that reflects how he did it; but he ought to have
then omitted the special, which is not very much simpler.

>"Plurimum abest, ut hoc problema aggredi ausim, ut potius, frustra in eo
>evolvendo desudasse, fateri cogar ; verum tamen casum observavi omnino
>singularem, ac simplicitate memorabilem, quo Lunae eiusmodi motus
>imprimi potuisset, ut perpetuo Soli, vel coniuncta, vel opposita,
>apparitura fuisset, cuius casus consideratio, cum forte usu in hoc
>difficillimo negotio non destituatur, haud displicitura videtur."
>
>I've changed "calus" to "casus".

Correctly, of course. My proof-reading remains assiduous but
inadequate.

>I am very far from daring to tackle this problem, nay rather I am
>forced to confess that I've sweated in vain over trying to solve it.
>However I have noticed a totally special case of memorable simplicity
>in which motion of such kind could have been stamped on the moon that
>it would have appeared in permanent either conjunction or opposition to
>the sun. Consideration of this case won't, I think, be displeasing
>since perhaps it is not without usefulness in this most difficult
>business.

That reads as if Euler had been speaking English to a group of friends
rather than writing it for publication, so I'll change "I've" to "I
have" and "won't" to "will not", and adjust around "permanent" :-

"I am very far from daring to tackle this problem, nay rather I am

forced to confess that I have sweated in vain over trying to solve it.

However I have noticed a totally special case of memorable simplicity in
which motion of such kind could have been stamped on the moon that it

would have appeared permanently in either conjunction or opposition to
the sun. Consideration of this case will not, I think, be displeasing

since perhaps it is not without usefulness in this most difficult
business."

That is now in <http://www.merlyn.demon.co.uk/euler304.htm>.

Again thanks.

--
(c) John Stockton, nr London UK Reply address via Home Page.
news:comp.lang.javascript FAQ <http://www.jibbering.com/faq/index.html>.
<http://www.merlyn.demon.co.uk/js-index.htm> jscr maths, dates, sources.
<http://www.merlyn.demon.co.uk/> TP/BP/Delphi/jscr/&c, FAQ items, links.

[B. T. Raven]

Die Wed Nov 28 2012 13:41:10 GMT-0600 (Central Standard Time) Dr J R
Stockton <repl...@merlyn.demon.co.uk.invalid> scripsit:

> In alt.language.latin message <k92k03$n3h$1...@dont-email.me>, Tue, 27 Nov
> 2012 14:50:11, Ed Cryer <e...@somewhere.in.the.uk> posted:
>
>
>> I did enjoy wrestling with "motus medius". I still don't understand it
>> but it appears to have gone the way of "phlogiston" and "ether".
>
> No; it's still in active use, but Englished. It even has a page
> <http://en.wikipedia.org/wiki/Mean_motion>. The Google translation of
> the Finnish version of the page is moderately amusing. The term occurs
> in the Google translation of <http://de.wikipedia.org/wiki/Satellitenbah
> nelement>, too. And the Italian page is "Moto Medio".
>
> See also in <http://en.wikipedia.org/wiki/Two-line_element_set> : ISS's
> TLE includes an element explained as
> 8 53–63 Mean Motion [Revs per day] 15.72125391
> which seems like a diurnal procession of nearly 16 dog-collars.

Is that dog-collars arcdegrees? In Latin it would be "mella" a
mellifluous word.

Eduardus

[Dr J R Stockton]

In alt.language.latin message <k96hd...@news7.newsguy.com>, Wed, 28
Nov 2012 20:31:21, B. T. Raven <btr...@nihilo.net> posted:

>Die Wed Nov 28 2012 13:41:10 GMT-0600 (Central Standard Time) Dr J R
>Stockton <repl...@merlyn.demon.co.uk.invalid> scripsit:
>
>> In alt.language.latin message <k92k03$n3h$1...@dont-email.me>, Tue, 27 Nov
>> 2012 14:50:11, Ed Cryer <e...@somewhere.in.the.uk> posted:
>>
>>
>>> I did enjoy wrestling with "motus medius". I still don't understand it
>>> but it appears to have gone the way of "phlogiston" and "ether".
>>
>> No; it's still in active use, but Englished. It even has a page
>> <http://en.wikipedia.org/wiki/Mean_motion>. The Google translation of
>> the Finnish version of the page is moderately amusing. The term occurs
>> in the Google translation of <http://de.wikipedia.org/wiki/Satellitenbah
>> nelement>, too. And the Italian page is "Moto Medio".
>>
>> See also in <http://en.wikipedia.org/wiki/Two-line_element_set> : ISS's
>> TLE includes an element explained as
>> 8 53–63 Mean Motion [Revs per day] 15.72125391
>> which seems like a diurnal procession of nearly 16 dog-collars.
>
>
>Is that dog-collars arcdegrees? In Latin it would be "mella" a
>mellifluous word.

No. Rev is short for Reverend, the style of clergymen in the Church of
England, and they commonly wear clerical collars which look something
like an ordinary collar back-to-front. That is commonly known as a dog-
collar. See <http://en.wikipedia.org/wiki/Dog_collar> paragraph 2. I
don't know what clergy wear in the CST region.

The mean motion of ISS is therefore, disregarding refinements, about
360*15.72 degrees per day.

--
(c) John Stockton, nr London, UK. E-mail, see Home Page. Turnpike v6.05.
Website <http://www.merlyn.demon.co.uk/> - w. FAQish topics, links, acronyms
PAS EXE etc. : <http://www.merlyn.demon.co.uk/programs/> - see in 00index.htm
Dates - miscdate.htm estrdate.htm js-dates.htm pas-time.htm critdate.htm etc.

[Dr J R Stockton]

In alt.language.latin message <eBZxb0Bu...@invalid.uk.co.demon.merl
yn.invalid>, Fri, 30 Nov 2012 19:15:58, Dr J R Stockton <reply1248@merly
n.demon.co.uk.invalid> posted:

>The mean motion of ISS is therefore, disregarding refinements, about
>360*15.72 degrees per day.

Time to provide the Christmas homework - last chunk but one before
completion.


My page <http://www.merlyn.demon.co.uk/euler304.htm#Enestrom304>, three-
column table.
Best original Latin
<http://archive.org/stream/novicommentariac10impe#page/545/mode/1up>.

Section 2, second sentence of two.

LATIN :

Quare etsi motus Lunae ex hac Theoria satis accurate est definitus, id
tamen potius singularibus circumstantiis, quae in Luna locum inveniunt,
est tribuendum, quam cuipiam perfectioni, ad quam Theoria evecta censeri
queat, si enim Luna bis vel ter longius a terra abesset, vel eius orbita
magis esset excentrica, omnes labores adhuc exantlati [ JRS: sic ] omni
fructu caruissent, ac ne nunc quidem eius motum obiter saltem ad certam
quandam regulam revocare liceret.

ENGLISH SO FAR :

Wherefore, although the movement of the Moon is determined with
sufficient accuracy by this Theory, but rather that the individual
circumstances, which in the case of the Moon are found, are to be
attributed, than any perfection to which the extended Theory can be
assessed, for if the Moon were removed twice or three times farther from
the earth, or its orbit were more eccentric,

ABOVE IS OK but possibly improvable.

all the labours of all the fruit of exantlati still deprived of [ JRS:
without all the labours of all the descendants of the Gods? or of Atlas,
if [ex]antlati be a typo for [ex]atlanti? ] [ EjH: (all the labours
of?) still those who suffered would have been deprived of all the fruit
] , now, indeed, at least in passing, and even the motion of this body
would be allowed to bring them back to a given rule.

AND THAT MAKES INSUFFICIENT SENSE.


After that, there remains only a part of the second sentence of section
4 to be fettled.

Merry Christmas, etc.

--

[Johannes Patruus]

Quick note: "exantlati" < exantlo = exanclo -
http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0059%3Aentry%3Dexanclo

Patruus

[Ed Cryer]

And so although the movement of the moon is defined with sufficient
accuracy by this theory, that fact is more attributable to singular
circumstances which have place in the moon than to any completeness to
which the theory might be thought to have been raised. For if the moon
were either twice or thrice its distance from the Earth, or its orbit
were less circular [1], then all the labours so far expended would have
lacked all success, and incidentally it wouldn't be possible even now to
reduce its motion to any fixed rule.

[1] Take "excentrica as "eccentric" and it has the same meaning as
"distance from the Earth".

Ed

Merry Christmas, Dr Stockton.
Are you coming to any conclusions about whether or not Euler ought to be
considered to have solved the question you mentioned earlier?

[Dr J R Stockton]

In alt.language.latin message <kb233i$lnn$1...@dont-email.me>, Fri, 21 Dec
2012 16:33:45, Ed Cryer <e...@somewhere.in.the.uk> posted:

**

>which the theory might be thought to have been raised. For if the moon
>were either twice or thrice its distance from the Earth, or its orbit
>were less circular [1], then all the labours so far expended would have

more eccentric

>lacked all success, and incidentally it wouldn't be possible even now

++++++++

>to reduce its motion to any fixed rule.

** "in" to me implies within, or perhaps on, the Lunar surface; and that
would not be right. Yours is undoubtedly more elegant, but I think mine
expresses the original meaning better.

++++++++ I feel sure that Euler might well have said "wouldn't", but
would have written "would not".

So far, I've added the new bit (after your [1]), attributed; but not yet
deleted my rubbish above; that is intended to imply that the matter
remains open but is now closable. I'm still contemplating your revision
of the part which I had thought good enough.

Thanks.

>[1] Take "excentrica as "eccentric" and it has the same meaning as
>"distance from the Earth".

I don't think that those two English terms are at all similar. Glance
at <http://en.wikipedia.org/wiki/Orbital_eccentricity>, and I think you
will see that "more eccentric" is, in this field, equivalent to "less
circular", and will be at least as easily understood by the intended (by
Euler, and by me) type of reader. In orbital mechanics, eccentricity is
not equivalent to weirdness.


ASIDE : Is the BBC radio theme music to "The Fosdyke Saga", i.e. the
Minuet from [Handel's] Berenice" by a well-known Brass Band,
played /lugubrioso/, on YouTube or elsewhere, and if so where?
Full minuet as such preferred.

>Merry Christmas, Dr Stockton.
>Are you coming to any conclusions about whether or not Euler ought to
>be considered to have solved the question you mentioned earlier?

I am satisfied that, in E.304, Euler effectively predicted Lagrange
Points L1 and L2 ; that with another quick think and a paragraph, he
could have predicted L3 ; and that the work nowhere considers anything
anywhere leading to finding L4 and L5.

What we are now doing is akin to the Chauffeur polishing the car before
taking the Master from his Country House to catch a train at the local
Town : it does not affect the result, but it ought to be done. After
the next section is done, a final overall review ought to be equivalent
to washing the tyres - no real improvement, unless a puncture is
noticed.

[Johannes Patruus]

On 22/12/2012 20:53, Dr J R Stockton wrote:

> ASIDE : Is the BBC radio theme music to "The Fosdyke Saga", i.e. the
> Minuet from [Handel's] Berenice" by a well-known Brass Band,
> played /lugubrioso/, on YouTube or elsewhere, and if so where?
> Full minuet as such preferred.

The only recorded brass band arrangement I could find anywhere is Track 2
of this CD -
http://www.amazon.co.uk/dp/B00000E2R5/

Patruus

[Ed Cryer]

Many people try to improve the meaning of the original in their
translations, and sometimes end up distorting it; often for polemical
reasons.
In this instance I have no doubt that Euler's "in Luna" means "in the
case of the moon", but he didn't write "in casu Lunae", he wrote "in Luna".

I write from experience. There's a claim that Plato differentiated the
two uses of the verb "to be" in one of his later books. This
differentiation is often believed to have been discovered by Kant, who
made much more hay out of it in his books.
Hhhmmm! But I notice strong national pride in the interchange on the
subject. And, of course, native-speakers of languages that use the
copula have added reasons that native-speakers of languages that don't
use it cannot condone.

Ed

[Dr J R Stockton]

In alt.language.latin message <ajnt9l...@mid.individual.net>, Sun,
23 Dec 2012 08:22:17, Johannes Patruus <inv...@invalid.invalid> posted:

Thank you; that's it, of course; but I wanted a URL for a Web page, for
which a page offering a single copy does not suffice.

Google "Minuet from Berenice" lists many versions on YouTube (I like
most of an Organ one; there is an Accordion one), but the Brass Band one
for Fosdyke was special.

--
(c) John Stockton, Surrey, UK. �@merlyn.demon.co.uk Turnpike v6.05 MIME.
Web <http://www.merlyn.demon.co.uk/> - FAQish topics, acronyms, & links.
Proper <= 4-line sig. separator as above, a line exactly "-- " (SonOfRFC1036)
Do not Mail News to me. Before a reply, quote with ">" or "> " (SonOfRFC1036)

[Dr J R Stockton]

In alt.language.latin message <kb74pt$dh5$1...@dont-email.me>, Sun, 23 Dec
2012 14:34:04, Ed Cryer <e...@somewhere.in.the.uk> posted:

>Dr J R Stockton wrote:
>> In alt.language.latin message <kb233i$lnn$1...@dont-email.me>, Fri, 21 Dec
>> 2012 16:33:45, Ed Cryer <e...@somewhere.in.the.uk> posted:
>>
>>> Johannes Patruus wrote:
>>>> On 20/12/2012 15:39, Dr J R Stockton wrote:
>>
>>>>> My page <http://www.merlyn.demon.co.uk/euler304.htm#Enestrom304>, three-
>>>>> column table.
>>>>> Best original Latin
>>>>> <http://archive.org/stream/novicommentariac10impe#page/545/mode/1up>.
>>>>>
>>>>> Section 2, second sentence of two.
>>>>>
>>>>> LATIN :
>>>>>
>>>>> Quare etsi motus Lunae ex hac Theoria satis accurate est definitus, id
>>>>> tamen potius singularibus circumstantiis, quae in Luna locum inveniunt,
>>>>> est tribuendum,
>>>>>

>>>>> ENGLISH SO FAR :
>>>>>
>>>>> Wherefore, although the movement of the Moon is determined with
>>>>> sufficient accuracy by this Theory, but rather that the individual
>>>>> circumstances, which in the case of the Moon are found, are to be
>>>>> attributed,

>>> And so although the movement of the moon is defined with sufficient
>>> accuracy by this theory, that fact is more attributable to singular
>>> circumstances which have place in the moon than to any completeness to
>> **

>> ** "in" to me implies within, or perhaps on, the Lunar surface; and that
>> would not be right. Yours is undoubtedly more elegant, but I think mine
>> expresses the original meaning better.

>Many people try to improve the meaning of the original in their
>translations, and sometimes end up distorting it; often for polemical
>reasons.
>In this instance I have no doubt that Euler's "in Luna" means "in the
>case of the moon", but he didn't write "in casu Lunae", he wrote "in
>Luna".

Could Euler have meant to write "in Lunae locus"? But none of the
sources support that.

>I write from experience. There's a claim that Plato differentiated the
>two uses of the verb "to be" in one of his later books. This
>differentiation is often believed to have been discovered by Kant, who
>made much more hay out of it in his books.
>Hhhmmm! But I notice strong national pride in the interchange on the
>subject. And, of course, native-speakers of languages that use the
>copula have added reasons that native-speakers of languages that don't
>use it cannot condone.

True. But in current English "in the moon" conveys a meaning which
Euler certainly cannot have intended, and is therefore inadmissible. It
must be remembered that Euler was writing c.18 European Latin rather
than Classical Latin, and that he was writing for scientists and
mathematicians. A modern translation must convey to moderns what the
original would have conveyed to contemporaries.

Example : nowadays (in the UK) unqualified "engine" means "motor" or
"locomotive", whereas a couple of centuries ago it was a non-derogatory
version of "contraption".

Is "which have place for the moon" supportable?