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.
पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४४२
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