पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४४०

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244 GANITASARASANGRAHA (then) divided by their sum. The(resulting) quotients, on being multiplied by the measure of the base (as a whole) give rise to the (respective basal) segments. These (measures of the segments respectively) multiplied in the inverse order by the quotients (obtained in the first instance as above), give rise (in each case} to the value of the inner perpendicular Examples in illustration thereof. 181छै. (The given) pillars are 16 hastas in height. The base (covering the length between the points where the string touch the ground) is pointed out to be 16 hostok. Give out, in this case, the numerical value of the segments of the base and also of the inner perpendicular. 182). The height of one pillar is 86 hosta8 ; that of the second is 20 heasta8. The length of the base-line is 12 lastus. What is the measure of the (basal) segments and what of the (inner) perpendicular ? 188-184ी. (The two pillars are) 12 and 15 hosts (respect. ively) ; the measure of the interval between the two pillars ia 4 hosts. From the top of the pillar of 12 lakkus a string is stretched so as to cover 4 hosta8 (along the basal line) beyond the foot of the other pillarFrom the top of (this) other pillar (which is 15 Masta8 in height) a string is (similarly) stretched so as to cover 1 ist (along the basal line) beyond the foot (of the pillar of 12 hosts in height. What is the measure of the (basal) segments here, and what of the inner perpendicular? 185. (In the case of a quadrilateral with two equal sides), each of the two sides is 18 ha88 in measure. The base here is 14 c1 a (e+ n) From these ration we get A (+) c1 a (c+ m) a (c+ ) (c+ I ++) c1 + c2 ८ (c+ m) + b(+ 1) ८ (e+ T) + b (c+ n) ४ (८+ ) (c+ m + ) Similarly 2 = ; and p=c2 x - -, or e = a (८+ m) + b (८+ ) c + c + m, 185J• Here a quadrilateral with two equal sides is given ; in the next stanza a quadrilateral with three equal sides, and in the one next to it a quadrilaterol with are given. In all these cases the diagonals of the condri. unequal sides lateral have to be first found out in accordance with the rule given in stanza