16 cies are called irrational (करणी ). These irrational lines and figures are the chief subject of the tenth book. They are divided into many classes of which 18 are bhe chief. They are as follows:- I. A medial line (मध्यरेखा ) is defined in Prop. 1. A rectangle which has its sides commensurable in power only shall be irrational and is called a medial superficies. The line bhe equare of which is equal to bhis figure is irrational and is called a media lineThus a medial line is an irrational line of which the square equals a rectangle contained by two re tional lines commensurable in power only. Propositions from 1 to 35 threat of the properties of medial line. It will be enough to note a few of these to shew bheir nature. *« A line commensurable to a media ine shall also be a medial line.'
- The difference between two medial superficies is irrationa.
To find out two medial lines commensurable in power only, containing in power a rational or a medial superf« cles. To find out two medial lines incommensurable in power the squares of which, added together, make a medial superficies and twice the rectangle of which is national.* II. A binomial line(बोगरे) is the next irrational line. It is treated first in Prop. 38. If the lines which are com mensurable in power only be added together, bhe line so formed shall be irrational and is called a binomial line. Thus a binomial line is an irrational line composed of two rational lines commensurable in power only. It is made up of two parts or names, of which one is greater than the other. The equare of one part is therefore greater bhan that of the other. This line is divided into six classes, ४%8, the first binomial line (प्रथम योगरेखा ), the second binomial line (द्वितीय योगरे) and so forth. The first three binomial lines (प्रथम द्वितीय and तृतीय are formed when the square of the greater line exceeds that of the less by the square of a line which is com mensurable in length to it, viz., bhe greater ; and the last three kinds of binomial lines (चतुर्थ, पक्षम, and षष्ठ योगरेला ) are formed when bhe square of the greater part exceeds the square of Propa 19, 20, 2, and Bl apectively.
