An example in illustration thereof.
109. O mathematician, calculate and tell me quickly the measures of the two (equal) sides, of the base and of the perpendicular in relation to an isosceles triangle derived with the aid of 3 and 5 as bījas.
The rule regarding the manner of constructing a trilateral figure of unequal sides :-
110.[1] Half of the base of the (oblong of reference) derived (with the aid of the given bījas) is divided by an optionally chosen factor. With the aid of the divisor and the quotient (in this operation as bījas), another (oblong of reference) is derived. The sum of the perpendicular-sides belonging to these two (oblongs of reference) gives the measure of the base of the (required) trilateral figure having unequal sides. The two diagonals (related to the two oblongs of reference) give the two sides (of the required triangle). The base (of either of the two oblongs of reference) gives the measure of the perpendicular (in the case of the required triangle).
An example in illustration thereof.
111. After constructing a second (derived oblong of reference) with the aid of half the base of the (original) figure (i.e. oblong of reference) derived with the aid of 2 and 3 as bījas, you tell (me) by means of this (operation) the values of the sides, of the base and of the perpendicular in a trilateral figure of unequal sides.
Thus ends the subject of treatment known as the Janya operation.
{{rule}
110. ^ The rule will be clear from the following construction:- Let ABCD and EFGH be the two derived oblongs, such that the base AD = the base EH. Produce BA to K so that AK=EF. It can be easily shown that DK = EG and that the triangle BDK has its base BK=BA + EF, called the perpendiculars of the oblongs, and has its sides equal to the diagonals of the same oblongs.
