पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/४५५

५HAPTER VII--CALCULATIONS REGARDING EXCAVATIONS. 259 Ecomplex + ४८ustration thereof. 5. In relation to (an equilateral) quadrilateral area (represent. ing the scotion of a regular excavation), the sides and the depth are 8 losts (each in measuro). In respect of this regular excava tion, what may be the value of the cubical contents here? 6. In relation to an (equilateral) triangular area (representing the section of a regular excavation), the sides are 82 \costs each, and in the depth there are found 86 last8 and 6 digulas. What is the calculation (of the contents) here ? 7. In relation to a (regular) circular area representing (the section of a regular excavation, the diameter is 108 hostesand the depth (of the excavation) is 165 heastes. (Now), give out what the cubical contents are. 8. In relation to a longish quadrilateral area (forming the Geotion) of a regular excavation, the breadth is 25 lastus, the side (measuring the length) is 60 hosts and the depth (of the ex. cavation) is 108 hosticsuickly give out (the cubical contents of this regular excavation) The rule for arriving at the accurate value of the cubical contents in the calculation relating to excavation, after knowing the result designated amitiko as well as the result designated aupta and with the aid of these results : 9-11]. The values of the base and the other sides of the figure representing the top sectional area are added respectively to the values of the base and the corresponding sides of the figure reprasenting the bottom sectional area. The (several) sums (so arrived at) are divided by the number of the sectional areas taken into consideration (in the problem). The (resulting) quantities are 9-11x. The figures dealt with in this rule are bruncated pyramids with rectangular or triangular bases, or truncated cones all of which have to be conceived as trned upxide down. The rule deals with bhree different kinds of measures of the cubical contents of excavations. Of these, two, viz., the Kavrmatika and Addro measures give only the approximate values of the contents. The accurate measure is calculated with the help of these values If K represents the Kormukiko-photo and A represents the Audro-photo ACK then the accurate measure is said to be equal to ah + K, 8.e., K + है A,