. Cyclomathesis : or, An easy introduction to the several branches of the mathematics; being principally designed for the instruction of young students, before they enter upon the more abtruse and difficult parts thereof . , then the equa-\j tion is/ 4- xc—ayd + xe-ayf 4- x&~*jb zz o,which is one way where one term is without x. Inlike manner, divide all by x°9 and the fecond termwill be without x, which is a fecond way. Againdivide all by xe9 and the third term will be withoutx. Alfo divide all by X&9 and the fourth term willbe without x. Hence the equation admits of asmany different forms as
. Cyclomathesis : or, An easy introduction to the several branches of the mathematics; being principally designed for the instruction of young students, before they enter upon the more abtruse and difficult parts thereof . , then the equa-\j tion is/ 4- xc—ayd + xe-ayf 4- x&~*jb zz o,which is one way where one term is without x. Inlike manner, divide all by x°9 and the fecond termwill be without x, which is a fecond way. Againdivide all by xe9 and the third term will be withoutx. Alfo divide all by X&9 and the fourth term willbe without x. Hence the equation admits of asmany different forms as there are terms, whereinthere are always one term without x. 2. Again, in the equation/4-^^J 4- xe—ajf+#s—*y, letting afide the firft term j*, the equationxc—aydjimXe-~ayfj^x&--ayk wji| admit of as many forms,where one term wants y9 as there are terms left, asappears by proceeding as in Art. I. Therefore if fbe the number of terras in the given equation ; thewhole number of forms, where one term is withoutx, and another without y9 is zz, t X t— 1. S c h o L. This fuppofes that all the indices are differentfrom one another •, but if feveral indices be the fame, -Ftp 84ABC 33 E ^ B A 7?D - C. Misccllcuues Art. XVIII. PROBLEMS. 429 fame, the number of transformations will be in fuch cafes, the number will neveramount to // — /. P R O B. IL A and B have each a number of fitillings -, and Asnumber is to Bs, in the ratio of 17,501501501 & infinitum, to 31-917171717 &c. ad infinitum ;and they are the leajt in that ratio: what are thenumbers ? By Prop. LVL Chap. III. B. II. Arithmetic, the circulating part 501 &c. zz vulgar fraction £21. 999 Alfo the circulating part 17 &c. zz IZ. There- 99 fore 17,501501 &c. zz 17 £21-, and &c. ~ —. Therefore As number is to Bs, as° 99 17 £21 to IZ, or as 153 + -— to -f- 999 * 99 J^ i 7 7484. ^17^-1 a. • —, or as -iur to ——•, that is, as J 02 2 240 to 11 111 11
Size: 1423px × 1756px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauthorada, bookauthorbostonpubliclibraryjohnadamslibrarybrl
