. 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 . But S. <Z AD/ zz -r-; therefore z OC —; whence -^z _ zz %z zyOC rad. curvature ~ (z being given). Whencex z*y(afluming the given quantity #) (xzx zz —, and ax* z]ythe fluent is — zz -^ which is correct, for in R,3 a z I ay zzo, and x zz o, whence # ^y — rz z]/y. For brevitys fake put — zz 1, then x zz yiz. But xz zzy\z% = y!#* + jylyj and \—y\ X x% zzy\y\ yiytherefore x z
. 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 . But S. <Z AD/ zz -r-; therefore z OC —; whence -^z _ zz %z zyOC rad. curvature ~ (z being given). Whencex z*y(afluming the given quantity #) (xzx zz —, and ax* z]ythe fluent is — zz -^ which is correct, for in R,3 a z I ay zzo, and x zz o, whence # ^y — rz z]/y. For brevitys fake put — zz 1, then x zz yiz. But xz zzy\z% = y!#* + jylyj and \—y\ X x% zzy\y\ yiytherefore x zz Put v zzyl, andv^zzy, x/i —yj QV^V then x zz ••* \ and the fluent is x zz 2 — VI—-VV 2 + t*z; y • vi—vv, for the nature of the curve RDB. 1 ■ Reduced 4* — xx zz 31^ + v& _- ^| 4. 4^. Cor. 1. If Q be the center of the curve, then CRzz 2CB. For when y is greateft, x zz z, and there-fore x (z) zzy\z, andyi zz 1, or y zz 1. Whencev zz 1, tfffJ v/i —vv zz. o, therefore x zz 2 -, /^/?V, CB zz 1, CRzz 2. Cor. 2. CB zz \a. Cor. 3. To conftrucl the curve, take any angle, find xits fine -7-, or y\ zz v, Then we have y zz v*, and 2 + vvx zz2 Vi—vv j and finding thcfe for any JFig. 7/r.
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