The next two verses reveal sciences of Algebra and Geometry.

When the numeral signifying unity is added to another such numeral it makes two, one and two make three, two and two make four, three and three make six. In the same way the numeral four, five, etc., occurring in this verses show that the science of mathematics is evolved by treating and figures in different ways, such as addition, etc.

The frequent use of the conjunction ‘cha’, and shows that there are many branches of this science. It is known to all that this science has been fully dealt with in Jyotishshastra which is a limb of the Vedas (Vedanga). For this reason we do not dilate upon it here. But it is to be remembered that such verses contain the germs of the science of mathematics which is the subject matter of the books on Jyotish

• (Astronomy). The science of Numbers (Arithmetic) deals with known, whereas the science of Algebra with unknown, and uncertain quantities. These verses suggest the latter science also by suggesting the symbols a3 – b, etc., Yajur Veda XVIII 24 and 25

According to the maxim that one act serves of

• a double purpose, the marks of short and long vowels given over the letters of this verse (SamaI.1.) contain an allusions to the science of Algebra.

There is a third branch of the mathematical science called Geometry which is alluded to in the following verses.

In these two verses the science of Geometry is referred to.

The vedi is to be made of a triangular, quadrilateral, circular shape or in the likeness of a Shyena bird. The purpose of the direction to make the vedi of various shapes is to suggest geometrical science. A line running round the parts of the earth farthest from it center is called the circumference.

A line drawn from any point on the circumference and passing through the center is called the diameter or the middle line in geometry. This line is the navel of the world, the earth and the universe, because all such lines converge to

• meet in the center so the yajna is the navel of the universe because it is to be resorted to (by all). Similarly, the other globes, the moon, etc., have their circumference, etc. The main-causing sun, light, heat and the air also, have got their circumferences in order to give them their (requisite) velocity. Their (of the sun, air, etc.) power in the shape of medicines is widespread. The Veda (Brahma) encompasses speech from within and without like a circumference. Yajur XXIII 62.

What is the true knowledge of all things, who is its possessor, and what is the intellect that is necessary for acquiring right knowledge? Who is the measurer, who measures and counts all? What is the cause and what is the essence, like ghee, in this world, which ought to be known or which is the destroyer of all suffering and the essence lubricated with happiness? What is the back-cover viz., the circumference (which is a line passing

• round a spherical object? What is the independent and what the praiseworthy object?

The answers to these questions are:-

The Supreme Lord whom the learned have worshipped, do and shall ever worship, knows everything as it is. He is the Measurer of all. The answers to the remaining questions are to be found out by construing the words of the verse in a similar manner. Rig VIII. 7.18.3.

[The word parijhi’ ‘circumference’ shows that here there is an allusion to the geometrical science. This science has been dealt with in detail in theJyotish-Shastra, the science of astronomy.]

The Vedas contain many verses which treat of the mathematical science.