18 Like a binomial line it has also six varieties. The first three kinds (प्रथम, द्वितीय, and तृतीय अन्तररेखा) are formed when bhe square of the whole line made up of the residual line and bhe line joined to it exceeds the square of the line joined by bhe square of a line commensurable to it in length; and the last three kinds (चतुर्थ, पक्षम and षष्ठ अन्तररेखा ) are formed when the square of the whole line made up of the residual line and bhe line joined to it exceeds the square of the line joined by the square of a line incommensurable to it in length. Propositions 82 to 87 teach how to find these lines. IX. A first medial residual line (प्रथममभ्यान्तररेखा ) is an irrational line which remainswhen from a medial ine is taken away a medial line commensurable to the whole in power only and the part taken away and the whole line contain a rational superficies Proposition 7 deals with it. X. The next proposition treats of the second medial residual line ( द्वितीयमध्यान्तररेला ) which is an irrational line which re, mainswhen from a medial line is taken a medial line commensurable to bhe whole in power only and the part taken and the whole line contain a medial superficies XLL A less line (न्यूनरेखा ), taught in Prop. 8, is an irrational line which remain, when from a right line is taken a line incommensurable in power, the square of the whole line and the square of the park taken together make a ra @ional superficies, and twice the rectangle contained by them makes a medial superficies XII. A line making with a rational superficies the whole superficies medial ( ) is an irrational line which remains, when from a right line is taken a right line incommensurable in power to the whole line and bhe square of the whole line and of the part taken together make a medial superficies and twice the rectangle contained by them is ra tional. This is treated of in Prop. 7. XIII. The last irrational line is taken up in bhe next Prop. (78). It is a line making with a medial superficies the whole superficies medial (मध्ययोगजमध्यरेख). It is an irrational
