पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४५८

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2822 GANITASARASANGRAHA here, gives rise to the value of the (required) perimeter in the case of triangular and circular excavations. In the case of a quadrilateral excavation, (this same value of the required pori moter results) by multiplying the quantity fou (with the value of the breadth as before). in the case of excavations having central masses tapering up wards or downwards the operation (for Komantikephala) is (to add the value of) half the breadth of the excavation to (that of the breadth of) the central nass, and (for Addrepala), to add (the value of) the breadth (of the excavation to the value of the breadth of the central mass); then (the procedure is) as (given) before. Ecomples *n allustration thereof. 21. The already mentioned trilateral, quadrilateral, and circular (areas) have ditches thrown round them. The breadth measures 80 dep¢8and the ditches are as much as 4 (data8) in breadth, and 8 (dan!c) in depth. (Find ont the cubical oontents.) and bhe excavation may be of the same width both at the bottom and the top, or may be of diminishing or increasing width. The rule enables us to find out the total length of the ditch in all these cases I. When the width of the ditch is uniform, the length of ditch = (d + b) * 3 in the case of an equilateral triangular or dircular ditch, where d is the nmeasure of a side or of the dinmeter of the central mas8 and b is the width of the ditch : but this length = (d + b) x 4 in the case of a square_oxcavation with a central mass, square in section. II. When the ditch is tapering to a point at the bottom or the top, the length of the ditch for finding out bhe Kurmatiko-phold = (d + ;) x 3, or |d +

  • 44, according as the central mass (1) is in section trilateral or circular, or (१)

Bqu8B Length of ditch for finding ou€A17ar-phold = (d + b) + 3 and (d + b)

  • 4 respectively:

These expressions have to be multiplied by half of the width of bhe ditch and by its depth for finding out the respective oubical photos, 'The formulas given above in relation to briangular and circular excavations give only approximate results. With the aid of the total length of the ditoh 8o obtained, the unbical contents are found out in the case of ditches with sloping sides by applying bho rule given in stanzas 3 to 11} above