पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४७९

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CHAPTER IX -CALCULATIONS RELATING To SHADOWS . 283 square of the (given) shadow. This (remainder) is to be multi plied by the sun of the square of the human shadow and one. (The quantity so arrived at) is to be subtracted from the square of the (given) shadow. 'The square root of this (resulting remain- der) is to be subtracted from the (given) measure of the shadow; and, when (the quantity thus obtained is) divided by (the sum of) one and the square of the human shadowthere results exactly the measure of the inclination of the pillar. An compl2 ४ blustration thereby. 34. 'I'he human shadow (at the time) is twice (the human height). The shadow of a pillar, 18 host8 in height, is 29 (hosts). What is the measure of the slanting of the pillar here? (General Example8). 85-87४. A certain prince, staying in the interior of a palace, was (at a certain moment in the course of a forenoon, desirous of knowing the time elapsed in the course of the day, as also the measure of the human shadow (in terms of the human height). Then, the light of the sun coming through a window at a height of 32 hdata8 in the middle of the eastern wall fell at a place on the western wall at the height of 29 hastra. The distance between those two walls is 24 host08. 0 mathematician, if you have taken pains (to acquaint yourself) with shadow-problems, calculate and give out the measure of the time elapsed bluen, on that day, and also the measure of the human shadow (at that time in terms of the human height). 88 39. At the time when, in the course of a forenoon, the human shadow is twice the human height, what, in relation to a (vertical excavation of) square (section) measuring 10 hasi8 in each dimension, will be the height of the shadow on the western wall caused by the eastern wall (thereof) ? 0 mathematician, give out, if you know, how you may arrive at the value of the shadow that has ascended up (a perpendicular wall). 353४This example bears on the rules given in stanzas 8 and 28 above 88-89}. This example has to be worked out according to bhe rule given in stana 1 above.