2oo Of the SOLIDS 



l5 a J . The fegment, therefore, intercepted between B and 



C, the line AC being x, is ^ a 3 —^l aJ x^ 4-^ x\ 



l 5 5 3 



This alfo gives ^ a 3 , for the content of the whole folid 



when x — o, the fame value that was found by another me- 

 thod at § vi. 



Now, if we fuppofe x to be = AA', and to be gi- 

 ven rz b, the folid content of the fegment becomes 



4l? # 3 — 2.5rtf T ^ T +-3 3 , which mud be made equal to the 

 15 5 3 



given folidity which we fhall fuppofe zzm 3 , and from this 



equation a, which is yet unknown, is to be determined. If 



u — * b 3 u -r 

 3 



rzm 3 , ox ~~ u — ^ b 3 u rz — and u • — ¥■ b T u 



*S 5 * 3 4 



- T 5^ 3 ._ 15 p 

 4^ 12 



The fimplelt way of refolving this equation, would be 

 by the rule of falfe pofition. In fome particular cafes it 



then, for a 3 we put u, we have % (— u — 3 b 3 u -f- I £ 3 \ 



may be refolved more eafily ; thus, if ^fL LL b 3 — o 



7T 12 ' 



a — 5. b T u = o, and « s = 2 £ T , that is « T = ^ b T ox a=z 



4 4 4 



IX. 



