पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४३८

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242 GAN ITASARASANGRAHA, the ratio values of the (various) parts* are (respectively) multiplied. To each of the products (eo obtained), the square of tho measure of the top-side (of the given figure) is added. The square root (of the sum so obtained) gives rise to the value of the base (of each of the parts). The area (of each part divided by half the sum of the values of the base and the top-side (thereof) gives in (the requisite) order the value of the perpeadicular (which, for purposes of approximate measurement is treated as the side). Ecomplex 49 illustration hereof. 176. IThe measure of the top-side is given to be 7 ; that of the base below is 28, and that of each of the (remaining) sides is 80. The area (included within such a figure) is divided between two so that each obtains one (share). What is the vylue of the base (to be found out here) ? 1774-1784. The measure of tble base (of a quadrilateral with two equal sides) is 162, and that of the top-side (thereof) is seen to be 18. The value of each of the (two equal) sides is 400. The area of this (figure so enclosed) is divided among 4 men. The parts obtained by the men are (in the proportion of) 1, 2, 3. and 4 respectively. Give out, in accordance with this propor. tionate distribution, the values of the area, of the base, and (of either) of the (two equal) 81des (in each case) 1794. The measure of the base (of the givon quadrilateral figure) is 80, that of the topside is 40 ; the measure (eitherof of ) AB (BC + AD) BC2- AD AB (BF+ AU ) EF2 -AD A B (B C + A D) m + I + G + ' B C–A D2 But m + आ + G + ¢ A E ( B R + AD) 3 R2-A D2 m (B C -A D') dy-b } E + AD * 10 + % m + आ + p+ ¢ m + + + 2 = 2 2nd D F = x m + 2 m + i + p + ५ Similarly the other formulas may also be verified

  • Although the text simply states that the quotient has to be multiplied by

the value of the parts, what is intended is that the quotient has to be multiplied by the number representing the value of the parts up to the top-side in each case. That isin the figure on the previous pageto arrive at GH, for instance, , d-b has to be multiplied by m + w and not by a merely im + आ + p + ५