Principles of Mathematics by Russel – 1903


“The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists in the analysis of Symbolic Logic itself” – Betrand Russel

The great  Principles of Mathematics is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premises and primitive ideas, and so to prove that mathematics is a development of logic.

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Sutra 7-Sankalana Vyavakalanabhyam -By addition and by subtraction


This is comparatively a simple one .This Sutra can be applied for solving equation in which x co efficient and y coefficient are interchanged

For eg:

9x – 7y = 40

7x – 9y = 24

Adding  , (9x – 7y) + (7x – 9y) = (40 + 24)

ie.   16x – 16y = 64

x-y=4

Subtracting,  (9x-7y) – (7x-9y)=(40 – 24)

ie.2x + 2y = 16

ie x + y =8

Now doing it again we will get  x=6, y=2

Sutra-6 , (anurupye) Shunyamanyath–If one is in ratio, other is zero


(आनुरुप्ये) शुन्यमन्यत

This sutra is to solve simple equations which has big numbers in it. See the example,

5x + 8y = 3

10x + 12y = 6

Here the x coefficients and the constants are in ratio, So we can consider the other one which is ‘y’ as zero.

So x=3/5

The explanation mentioned above is a simple one. This sutra is also used for solving complex problems. It also has a sub- formula (sutra) ‘by addition and by subtraction’