. 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 . ill in the circle. Exam. Let AFZR be a cubic parabola, whofe equationis x zzj?. Here IT zz %x, and FT zz x/yy+yxx •—————— I—1—QV2, T zz s/yy+gy6. And R zz —g±—, whence F^ 13 FT* yy-fqf>H T fo 6yxy* as or as ^_L^__ x l3 zz J J ©r FI4R v4 l+9jshr jy+ as 6 a given quantity. Therefore F^ is every the fame, and the curve Sg is alfo a cubic parabola, the fame with the for
. 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 . ill in the circle. Exam. Let AFZR be a cubic parabola, whofe equationis x zzj?. Here IT zz %x, and FT zz x/yy+yxx •—————— I—1—QV2, T zz s/yy+gy6. And R zz —g±—, whence F^ 13 FT* yy-fqf>H T fo 6yxy* as or as ^_L^__ x l3 zz J J ©r FI4R v4 l+9jshr jy+ as 6 a given quantity. Therefore F^ is every the fame, and the curve Sg is alfo a cubic parabola, the fame with the former, but in a higher pofition. After the fame manner if AFZ be a biquadratic parabola, where a:™y4, there will come out Fg as y j and therefore the height at the vertex is o. PRO P. XIV. Prob. 2gw To invefligate and confirucl the curve or arch AFZ,by whofe revolution a vault AZR is formed, uponwhich the wall or building APQR being erecled, andbeing bounded by the horizontal line PQ, the heightZS being given; all the parts may remain in e*quilibrio. Draw ZG parallel to QSP, and let SZ zz ay Zizzx, Fizzy, AC=£, ZC=*. Then Fgzza+ay xbut (by Cor. r. Prop. XIII.) Fg is as —•; whence XT. _*. A^ -%• 3- \ :r
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