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

Page 449

252
GANITASĀRASANGRAHA.
An example in illustration thereof. 2111-2121. The man who travels to the east moves at the rate of 2 yõjanas (a day); and the other man who travels northwards moves at the rate of 3 yojanas (a day). This (latter man) having thus moved on for 5 days turns to move along the hypotenuse. In how many days will he meet the (other) man ? Both (of them) move out at the same time, and the number of days spent (by both of them) in journeying out is the same.
The rule for arriving at the numerical value of the diameters of circles described about the eight kinds of figures consisting of the five kinds of quadrilateral figures and the three kinds of triangular figures (already mentioned) :
2131. In the case of a quadrilateral figure, the value of the diagonal (thereof), divided by that of the perpendicular, and (then) multiplied by that of the lateral side, gives rise to the value of the diameter of the circumscribed circle. In the case of a trilateral figure, the product of the values of the two sides (other than the base) divided by the value of the perpendicular (gives rise to the required diameter of the circumscribed circle).
Examples in illustration thereof. 2141. In the case of an equilateral quadrilateral figure having 3 as the measure of each of its) sides, and also in the case of another (quadrilateral figure) of which the vertical side measures 5 and the horizontal side measures 12, what is the measure of the diameter) of the circumscribed circle ?
213). Let ABC be a triangle inscribed in a circle, AD the diameter thereof, and BE the perpendicular on AC. Join BD. Now the triangles ABD and BEC are pimilar. .. AB: AD=BE: BC
ABX BC
:. AD =
BE
This is the formula given in the rule A for the diameter of a circle circumscribed about a quadrilateral or a triangle.