15 r comprises 88 propositions. The Tenbh Book, which is generally considered as the hardest of all the books to understand, threats of lines and other magnitudes rational and irrational, but parti cularly of irrational magnitudes commensurable and incom. mensurable. Magnitudes (e. e. lines, superficies and solids ) are called मिलित or commensurable, if they have a common measure and are भिन्न or incommensurable if they can not be measured by a common measure. If the squares of lines can be measured by the self-same area, the lines are commensurable in power, and the lines whose squares are not measurable by the same area are or incommensurable in power. If there is a line supposed and laid before uB, of any length we please, if this line thus first set forth is imagined to have such divisions and so many parts as we list, 3, 4, 5 and so forth, which may be applied to any kind of measure, inches, feet and such others, and if to bhis line thus first supposed and set forth be compared a number of lines, some of these will be commensurable and some incommensurable : and of com mensurable lines some will be commensurable both in length and power and some commensurable in power only; and of incommensurable lines some will be incommensurable in length and some incommensurable both in power and length. The first line so set, to which and to the squares of which other lines and squares are compared, is called a ra tional line ( अकसंशईरेला ). Lines which are commensurable to this line, whether in length and power or in power only, are also rational; the square which is described on the rational right line supposed is rational; and the squares which are commensurable to this square are also rational. Thus the line which is first supposed and set forth, the lines which are commensurable to it, the square on it, and such superficies as are commensurable to the square are all rational and constitute what is called मूलदराशि. The rational line is the basis of most of bhe propositions of the tenth book from the tenth proposi. 'he line which is incommensurable to the first line sup and set forth, the superficies which is incommensurable to the square (& e. the square described on the rational line and the line the square of which shall be equal to bhat superf.
