Ganitasara Sangraha

SR No.: 020800
Original Sutra Author: N/A
Author: Mahaviracharya, M Rangacharya
Publisher: Government of Madras
Publication Year: 1912
Total Pages: 523
Language: Hindi, Sanskrit
Classification: Book_Devnagari
File Size: 22 MB

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192
GANITASĀRASANURAHA.
The rule for arriving separately at the numerical measures of the circumference, of the diameter, and of the area of a circular figure, from the combined sum obtained by adding together the approximate measure of its area, the measure of its circumference and the measure of its diameter :
30. In relation to the combined sum of the three quantities) as multiplied by 12, the quantity thrown in so as to be added is 64. Of this (second) sum the square root diminished by the square root of the quantity thrown in gives rise to the measure of the circumference.
An example in illustration thereof. 31. The combined sum of the measures of the circumference, of the diameter and of the area (of a circle) is 1116. Tell me what the measure of the) circumference is, what (that of) the caloulated area and what (of) the diameter is.
The rule for arriving at the practically approximate value of surface-areas resembling (the longitudinal sections of the yava grain, (of) the mardula, (of) the panava, and (of) the vajra ---
32. In the case of areas shaped in the form of the yava grain, of the muraja, of the panava and of the vajra, the
30. This rule will be clear from the following algebraical representation :Let c be the circumference of the circle. Ast is taken to be equal to 3,
is the diameter and is the area of the circle. If m stands for the combined sum of the circumference, the diameter and the area of the circle, then the rule given in the stanza to the effect that ca 12 m + 64 – N 64 may be easily arrived at from the quarratic equation containing the data in the problem :- C + + 3 =m.
32. Muraja means the same thing as marda la and mrdanga. The shape of the various figures mentioned in this stanza is as follows:
o CRD
Yavākārakņētra.
Morajākārakşětra.
Paņavākāraksētra.
Vajrākārakşötra