Ancient Mathematical Treatises
Ancient Mathematical Treatises
Jyotisa, as we have seen, consists of three sections. There was a scholarly man in the Matha who was particularly learned in this science. We wished to honour him with a title and decided upon "Triskandha- Bhaskara". "Skandha" literally means a big branch springing from the trunk of a tree. The three skandhas of Jyotisas are: siddhanta, hora and samhita.
The siddhanta-skandha deals with arithmetic, trigonometry, geometry and algebra. The higher mathematics developed by the west in later centuries is found in our ancient Jyotisa.Arithmetic, called "vyakta-ganita" in Sanskrit, includes addition,subtraction, multiplication and division. "Avyakta-ganita" is algebra. "Jya"means the earth and "miti" is method of measurement. "Jyamiti" evolved with the need to measure the sacrificial place:"geometry" is derived fromthis word. The "geo" in geography is from "jya". There is a mathematical exercise called "samikarana" which is the same as "equation".
The sixth Anga of the Vedas, Kalpa (I will speak about it later ), has a great deal to do with the fifth, that is Jyotisa. Kalpa has a section on "sulbasutras". These sutras mention the precise measurements of the "yajnavedi" (sacrificial altar). The character of the yajnabhumi is called "cayana". The sulba- sutras deal with a number of cayanas like, for instance, the one shaped like Garuda. They tell us how to construct a brick-kiln ---the number of bricks required for the cayana of such and such shapes. The siddhantaskandha is used in all this.
There is an equation in the Apastamba sulba sutras which could not be proved until recently. Westerners had thought it to be faulty merely as they could not solve it. Now they accepted it as right. That Indians had taken such great strides in mathematics; thousand of years ago has Later Bhaskaracarya wrote a mathematical treatise and named it "Lilavati" after his daughter. The father taught his widowed daughter mathematics and she became highly proficient in the subject. Lilavati deals with arithmetic, algebra, etc. It is a delightful book in which the problems are stated in verse as stories. Bhaskaracarya also wrote theSiddhanta-Siromani which deals with how the positions and movement of the heavenly bodies are determined.
We learn the text of an edict in the Pracinalekhamala that a Gurjara (Gujarat) king had made an endowment to popularise the works of Bhaskaracarya.Parts 7, 8, 9 and 10 of Euclid's Geometry are believed to be lost. All the 12 books on mathematics in Sanskrit are still available. "Making additions several times is multiplication; carrying out subtraction several times is division. " We remain ignorant of such easy methods of calculations dealt with in our mathematical texts.
Varahamihira lived several years before Bhaskaracarya, that is about 1,500 years ago. He wrote a number of treatises including the Brhat-Samhita and the Brhajjatika. The first is a digest of many sciences, its contents being a wonderful testimony to the variety of subjects in whichour forefathers has taken strides. Brhajjatika is all about astrology.
