282 GANITASĀKASANGRAHA. An example in illustratwit thereof. 29. The combined sum of the (height) measure of the style and the (length) measure of its shadow is 50. What may be the height of the style, the human shadow being (at the time) 4 times (the human height) ? The rule for separating the (length) measure of the shadow of the style and the measure of the human shadow (in terms of the human height) from (their) combined sum :- 30. The combined sum of the measures of the shadows of a style and of a man is divided by the (kurwn height) measure of the style as increased by one. The quotient (so obtained) is the measure of the human shadow (in terms of the human height) The combined sum (above-mentioned) as diminished by this (measure of the human shadow) gives rise to (the lergt measure of) the shadow of the style. An example in illustratwn thereof. 31. The height of a style is 10. The sum of the human shadow (in terms of the human height) and (the length of) the shadow of the style is 55. How much is the measure of the human shadow (in terms of the human height and how much is the length of the shadow of the style) ? The rule for arriving at the measure of the inclination of a pillar (or vertical style) :- 32-33. The product of the square of the human shadow and the square (of the height) of the style is to be subtracted from the 32-33 Let AB represent the position of a slanting pillai, and AC its shadow, and let AD be the same pillar in the vertical D position and AE its shadow. B Then AE G AD is equal to the ratio of the shadow of a man to his height at the time; and let this ratio be r. BG, the perpendicular from B on AD, represents the amount of slanting of the pillar, AB. It can be easily 1 shown that AD NAB²-BG2 AC BG A j' it can be seen. that AC-AC²-(AC-AB³ x ³) (²+1). The rule here gives this y² +1 From this BG= same formula. = E C
