पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४४२

246 GANITASARASANGRAHA (figure) strings are stretched out ¥o as to reach the middle point of the opposite) sides, (bhis being done) in respect of all the four sides. What may be the measure of each of the strings so stretched out ? In the interior of such (a quadrilateral figure with strings so stretched out, what may be the value of the iner) perpendicular and of the basal segments (caused thereby)? The measure of the height of the pillar is known. For, some reason or other that pillar gets broken and (the upper part of the broken pillar) falls (to the ground, the lower end of the broken off part, however, remaining in contact with the top of the lower part). Then the basal distance between the foot of the pillar and its top (now on the ground) is ascertained. And (here is ) the rule for arriving at the numerical value of the measure of the remaining part of the pillar measured from its foot : 190]. The half of the difference between the square of the total height and the square of the (known ) measure of the basal distance, whe divided by the total height, gives rise to the measure of what remains unbroken. What is left thereafter (out of the total height) is the measure of the broken part. Ecomple8 #n Justration thereof. 1914. The height of a pillar is 25 data8. It is broken some where between (the top and the foot). he distance between the (fallen) top (on the floor) and the foot of the pillar is 3 hostus. How far away (from the foot) is it (viz., the pillar) broken ? 190. If A B C is a right-angled triangle, nd if the measures of AC and of the sum of AB and BC are given, then AB and BC can be found out from the fact that BC 2 = AB9 + AC४. The for mula given in the rule is (AB+ RC) – ACK A B 2 (AB+BC) and this can be easily proved to be true from the above equality.