पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/४६४

GANITASĀRASANGRAHA. 266 ten, gives rise to the accurately calculated cubical contents of the pyramidal excavation. An example in illustration thereof. 31. Calculate and say what the approximate value and the accurate value of the cubical measure of a triangular pyramid are, the side of the (basal) triangle whereof is 6 in length. When the pipes leading into a well are (all) open, the rule for arriving at the value of the time taken to fill the well with water, when any number of optionally chosen pipes are together (allowed to fill the well). 32-33. (The number one representing) each of the pipes is divided by the time corresponding to each of them (separately); and (the resulting quotients represented as fractions) are reduced so as to have a common denominator; one divided by the sum of these (fractions with the common denominator) gives the fraction of the day (within which the well would become filled) by all the pipes (pouring in their water) together. Those (fractions with the common denominator) multiplied by this resulting fraction of the day give rise to the measures of the flow of water (separately through each of the various pipes) into that well. An example in illustration thereof. 3 There are 4 pipes (leading into a well). Among them, each fills, the well (in order) in,,, of a day. In how much of a day will all of them (together fill the well, and each of them to what extent) ? In the Fourth Subject of Treatment named Rule of Three, an example (like this) has (already) been given merely as a hint; the a gives the measure of the altitude of the pyramid as also of a side of the basal equilateral triangle. It may be easily seen that both these values are somewhat wide of the mark, and that the given approximate value is nearer the correct value than the Bo-called accurate value,