>>>>>>> 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.

>>>>> Believe it or not but I think I've come up with a fair translation of
>>>>> this.

>>>> 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

>>> 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 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'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.

>> 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

> (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)".
> "Eo casu quo" easliy transmutes to "quo casu ubi (cum)".

> (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

>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"

>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'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>.

>> In alt.language.latin message<acglirFkit...@mid.individual.net>, Wed,
>> 26 Sep 2012 16:34:23, Johannes Patruus<inva...@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?

>> In alt.language.latin message <acglirFkit...@mid.individual.net>, Wed,
>> 26 Sep 2012 16:34:23, Johannes Patruus <inva...@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?

>**********************

>  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.

> 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.

> 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.

> 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.

>"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.

>> 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".

>[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.

>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.

>> 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).

>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.

>> 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."

> "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?

>>> 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

>  > 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

>> 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>

>>> 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

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

>> Ed Cryer wrote:
>>> 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

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

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

>>> Ed Cryer wrote:
>>>> 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

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

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

> 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 wrote:
>>>> 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

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

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

> 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".