Bhaskaracharya —Leelavathi

[Shekhar Murthy]

Dear Learned Members,

I  shall be grateful if any learned member can give the Sloka , referred below, in Samskrtam, which is supposed to be in the above work of the great Rishi Bhaskaracharya

Quote : 

*Bhāskarāchārya*  *(1114 -1185 CE)*, has been called the greatest mathematician of medieval India. 

He was born in *Bijapur* in Karnataka, and is considered the progenitor of Differential Calculus - 500 years before Newton and Leibniz.

Bhāskarāchārya wrote at least four mathematical treatises in Sanskrit. 

One of them, titled Leelavati, contains many algebra-related teasers in this book, which have become the subject of significant research by scholars. These teasers are in the form of *shlokas* which pose problems. 

The shlokas need to be interpreted correctly to decipher the meaning in order to find the solution.

There is one Sloka in it ,  The direct meaning of this shloka is a question formulated as follows:

During the battle between Arjuna and Karna in Mahabharata, Arjuna released some arrows. Out of all the released arrows:

• Half were consumed in stopping the arrows coming from Karna,

• 4 times the squareroot of the arrows were consumed to control the horses of Karna's chariot.

• 6 were for gaining control over Shalya, the charioteer of Karna. (Shalya was the maternal uncle of Nakula and Sahadeva.)

• 3 were used to take on the umbrella of the chariot, flag of the chariot and bow of Karna.

• Finally Karna was killed with a single arrow.

🤔

So how many arrows were released by Arjuna in the battle?

Basic algebra easily yields the answer to this question, if the equation is formulated correctly.

Let the total number of arrows be X. 

The statements above can be reduced to the algebraic form

*X = X/2 + 4√X + 6 + 3 + 1*

If we solve this we get the value of X=100 for the number of arrows shot by Arjuna.

However, the fun is not just getting the algebra right. There is so much of hidden information in this shloka. 

If we pause to think a little deeper about the hidden meanings:

• Even for an atirathi like Arjuna, it took as many as 50 arrows to stop the arrows of Karna - it tells us about the skills of Karna.

• That the horses needed 40 arrows to immobilize the chariot tells us about the kind of training given to the horses in the battle field.

• When even the horses needed 40 arrows, that Shalya the charioteer surrendered with just 6 tells us that he is favouring Arjuna.

• 3 arrows to take the chariot and the bow shows the helplessness of Karna.

• Once everything is in control, the enemy should vanquished in just a single arrow.

Best Regards 

Shekhar Murthy

[Mohan Chettoor]

These two pages contain the sloka (which you mentioned)   and its translation in sanskrit. Here is the link:  https://archive.org/details/in.ernet.dli.2015.479162. You can trace the sloka in page 140/141. Best wishes.

Mohan Chettoor.

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[Anunad Singh]

पार्थ: कर्णवधाय मार्गणगणं क्रुद्धो रणे संदधे 
तस्यार्धेन निवार्य तच्छरगणं मूलैश्चतुभिर्हयान् |
शल्यं षड्भिरथेषुभिस्त्रिभिरपि च्छत्रं ध्वजं कार्मुकम् 

चिच्छेदास्य शिरः शरेण कति ते यानर्जुनः संदधे || ७६ ||

( गुणकर्म )

On Tue, Mar 16, 2021 at 12:10 PM Shekhar Murthy <smshekh...@gmail.com> wrote:

[Anunad Singh]

What should be the literal meaning of महामायूरी,  'The great peacock' or 'she who is riding a top a peacock' ?

On English Wikipedia (https://en.wikipedia.org/wiki/Mahamayuri), the meaning of महामायूरी is given as 'great peacock' .

-- anunAda

[Alankar Sharma]

Hi Shekhar ji,

Deducing and finding the "Hidden Meaning" out of the Lilavati example, I think is "AtiRanjanA". From a mathematical example we should not derive at such matter. For this we have  "MahaBharata", Which is "Original" story of Arjun and Karn.

Please don't take it otherwise, just me mati.

Alankar Sharma

[smshekh...@gmail.com]

Mahaan Santoshaha Mahoday. Dhanyavadaha.

 

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[smshekh...@gmail.com]

Mahaan Santoshaha Mahoday. Dhanyavadaha

 

Sent from Mail for Windows 10

 

From: Mohan Chettoor
Sent: 16 March 2021 14:44
To: sams...@googlegroups.com
Subject: Re: [Samskrita] Bhaskaracharya —Leelavathi

 

These two pages contain the sloka (which you mentioned)   and its translation in sanskrit. Here is the link:  https://archive.org/details/in.ernet.dli.2015.479162. You can trace the sloka in page 140/141. Best wishes.

Mohan Chettoor.

To view this discussion on the web visit https://groups.google.com/d/msgid/samskrita/CAAdWWbehgmFUso9xZZzLRX%3D3RFXss%2B8anyQ7S5b6uyoWo0niew%40mail.gmail.com.

 

[suman chakraborty]

धन्यवाद महोदयः

To view this discussion on the web visit https://groups.google.com/d/msgid/samskrita/293A2F81-3317-4BD7-AFDB-89516FB18116%40hxcore.ol.

[Shekhar Murthy]

Dear Shri Alankar Sharmaji

Namaste.  Yes. Thanks.  You are correct. Agree that Algebraic equations of Leelavathi are just for algebra

I am very greatly benefitting by all the previous inputs and advise from the highly learned members of the group

My humble Pranaams 

Shekhar Murthy 

Regards 

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[Shekhar Murthy]

Typo mistake . Instead of “ previous “ , Kindly read “ precious “

On Wednesday, March 17, 2021, Shekhar Murthy <smshekh...@gmail.com> wrote:

Dear Shri Alankar Sharmaji

Namaste.  Yes. Thanks.  You are correct. Agree that Algebraic equations of Leelavathi are just for algebra

I am very greatly benefitting by all the previous inputs and advise from the highly learned members of the group

My humble Pranaams 

Shekhar Murthy 

Regards 

On Tue, 16 Mar 2021, 21:34 Alankar Sharma, <sharma....@gmail.com> wrote:

Hi Shekhar ji,

Deducing and finding the "Hidden Meaning" out of the Lilavati example, I think is "AtiRanjanA". From a mathematical example we should not derive at such matter. For this we have  "MahaBharata", Which is "Original" story of Arjun and Karn.

Please don't take it otherwise, just me mati.

Alankar Sharma

On Tuesday, March 16, 2021 at 5:18:21 PM UTC+5:30 अनुनाद सिंह: wrote:

What should be the literal meaning of महामायूरी,  'The great peacock' or 'she who is riding a top a peacock' ?

On English Wikipedia (https://en.wikipedia.org/wiki/Mahamayuri), the meaning of महामायूरी is given as 'great peacock' .

-- anunAda

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[Anunad Singh]

Is Leelaavatii (or the whole of siddhaantashromaNi) available in

Unicode Devanagari / any other Indian script,

or,

any Roman form which can be converted to Unicode Devanagari,

or,

any legacy text format which can be changed to Unicode Devanagari?

That it is available in image format (scanned text), is well known.

-- anunAda

[ken p]

https://books.google.com/books?id=AoX5q7JjM2kC&printsec=frontcover#v=onepage&q&f=false

[Shreevatsa R]

GRETIL would be one of the first places to check, and it's available there: http://gretil.sub.uni-goettingen.de/gretil.html#Lilavati

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[Anunad Singh]

dhanyavaadaH Shreevatsa ji. It is relatively a new addition in GRETIL and was not there when I searched GRETIL last time.

-- anunAda

To view this discussion on the web visit https://groups.google.com/d/msgid/samskrita/CAKEM%3DPP4XJHHoZf2hEThz%3DJLtxwRQipf0_gvsc1ZbN6KKzXbfw%40mail.gmail.com.

[Anunad Singh]

Fortunately, बीजगणित, the second part of सिद्धान्तशिरोमणि  is also available at GRETIL. But I have still not found  ग्रहगणित  and गोलाध्याय‎ the third and the fourth parts.

-- anunAda

[ken p]

https://www.sanskritworld.in/index/listview/category_id/astronomy-astrology-and-mathematics#/page/