Decoding Baudhayana’s Sulbasutra..
Meet Pythagoras’ Predecessor
A friend had prodded me to look into this verse. Did it actually spell out the famed Pythagoras Theorem?
I did hear about Baudhayana’s sulbasutra. It was predating Pythagoras' theorem and was in the context of constructing Vedic Altars. My knowledge was limited to that. Here comes the chance to inspect it.
दीर्घचतुरश्रस्य अक्ष्णया रज्जुः पार्श्वमानी तिर्यग्मानी च यत् पृथग्भूते कुरुतः तदुभयं करोति ।
At first glance, I could just recognize the familiar diction of numbers, some Yoga Pose terminology and conjunctions.. Bollywoods numbers on ‘tirchi’/tirchi topi wale.. tirchi nazaar.
long, four, rope, sidewise, cross wise, measurement.. that which is done in parts is done by this..
दीर्घ long..चतुर four ..रज्जुः rope ..पार्श्व side..तिर्यक् tirchi/slanting..पृथक् seperate..उभयं both sides
The connectors
यत् तत् that which/that, च andVerbs
करोति, कुरुतः does [singular, plural]
I was unsure which Image it was hinting at. With inadequate diction and grammar, and without latching on to an image, one could hallucinate and over-fit anything. I had two images popping into my mind.
a) The Standard Right Angled Triangle
b) A smaller Square tilted and inscribed in a bigger Square.. In my high school library, learned this easy derivation of Pythogoras Theorem, and this method was attributed to Indian Math.
With the scattered words that I understood, I was not able to decode either of these pictures. Hence resorted to check with my erudite Sanskrit friend.
Wow! It was neither of the two images that I had painted in my mind. Infact, the verse describes a Rectangle, with an axial diagonal running through the opposite corners.
In the Rectangle, the measure of the diagonal is same as the measure of horizontal and measure of vertical both put together.
दीर्घचतुरश्रस्य अक्ष्णया रज्जुः पार्श्वमानी तिर्यग्मानी च यत् पृथग्भूते कुरुतः तदुभयं करोति ।
Let us examine the words again. Does it convey Phythogoras' Theorem directly? Or does it Hint it?
दीर्घचतुरस्र = rectangle,
अक्ष्णया रज्जुः = axial diagonal rope,
पार्श्वमानी = measure on the perpendicular side,
तिर्यग्मानी = measure on the lateral side,
यत् पृथग्भूते कुरूत = as computed seperately, तदुभयं करोति = is same as both sides put together
The rope corresponding to the the diagonal of a rectangle makes whatever is made by the lateral and the vertical sides measures individually.
Well, at least the image fits the description. For the Lack of technical language, I did not recognize the Rectangle. But it did not clearly mention was about the square part or the area part of the sides. It only mentions मानी which means ‘measure’. It could be length, square, cube of the sides, etc.
Unless the “squaring” “area” is encoded in the context of the problem statement. Ofcourse only Square would work though. Was it implicitly encoded? As it was in the domain of Shapes and Construction of Vedic Altars?..
And interestingly the root ‘ma’ means to measure, and a gamut of math words stem from this root. Math, limit, metre, matriculate, map and nimitt, amit, parimaaN, prameya, map chitra and so on..
I again hit on my Sanskrit friend on my inability to infer square/area in Baudhayana’s verse, and she shared the Kātyāyana version of the Sulba Sutra..
दीर्घचतुरश्रस्य अक्ष्णया रज्जुः तिर्यग्मानी पार्श्वमानी च यत् पृथग्भूते कुरुतः तदुभयं करोति इति क्षेत्रज्ञानम् ।
Words are exactly the same as in Baudhayana Sutra, but the word क्षेत्रज्ञानम् ‘area’ added.. And Bang.. This puts the verse in better comprehension without much room for ambiguity. I would n’t say lucid comprehension.. Maybe the order of verbs still in some doubt? I will park it though..
Like the High School days of signig off at the end of a proof.. QED.. End of Topic.. quod erat demonstrandum.. Or may be.. Om Tat Sat..
Baudhayana Maharshi might not have anticipated that after thousands of years, every word of his would be examined by this minion in Sanskrit, and from a different domain and world. Shri Gurubhyoh Namah!
References
- Fire Altars in Vedic Period in various shapes
2. Dr Vanishri Bhat’s lecture
https://youtu.be/5YfRXLf9q4E?si=ulzWiNWnFsBa-Gsc
