Practical arithmetic : by induction and analysis . increasing each of the three sides equally, there will berequired 3 oblong solids, C, c, c, of the same length as each ofthe sides, and whose thickness and hight are each the same as theadditional thickness; and also a cube, D, whose length, breadth,and hight, are each the same as the additional thickness. Hence, the solid contents of the first three rectangular solids,the three oblong solids, and the small cube, must together be equalto the remaining cubes (5824). Now find the thickness of the additions. It will always besomething less than t
Practical arithmetic : by induction and analysis . increasing each of the three sides equally, there will berequired 3 oblong solids, C, c, c, of the same length as each ofthe sides, and whose thickness and hight are each the same as theadditional thickness; and also a cube, D, whose length, breadth,and hight, are each the same as the additional thickness. Hence, the solid contents of the first three rectangular solids,the three oblong solids, and the small cube, must together be equalto the remaining cubes (5824). Now find the thickness of the additions. It will always besomething less than the number of times the trial divisor (1200) iscontained in the dividend (5824). Fio. 2, By trial we find 1200 is contained 4times in 5824. Place the 4 in the quo-tient, and proceed to find the contentsof the different solids: these addedtogether, make the number to be sub-tracted, called the subtrahend. The solid contents of the first threeadditions, B, B, B, are found, (Art. 93)by multiplying the number of sq. in. in the face by the thickness j. CUBE ROOT. 289 now there are 400 sq. in. in the face of each, and 400 X 3 = 1200 in one face of (lie three; then multiplying by 4, (the thickness,)gives 4800 cu. in. for their contents. The solid contents of the three oblong solids, C, c, c, are found(Art. 93; by multiplying the number of sq. in. in the face by thethickness; now there are 20 X 4 ^= 80 sq. in. in one face of each,and 80 X 3 = 240 sq. in. in one face of the three ; then multiplyingby 4, (the thickness,) gives 960 cu. in. for their contents. Lastly, find the contents of the small cube, D, by multiplying itslength (4) by its breadth (4), and that product by the thickness (4);this gives 4 X 4 X 4 = 64 cu. in. additions. If the solid contents of the several B B B =4800cu. be added together, their sum, q q (, __ ogQ6824 cu. in., will be the number of D = 64 small cubes remaining after forming the first cube, A. ^^^ 5824 Hence, when 13824 cu. in. are arrang
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectarithmetic, bookyear1
