Volume 1

Arithmetica universalis : sive de compositione et resolutione arithmetica liber / Auctore Is. Newton. [Anon].

  • Isaac Newton
Date:
1722
Catalogue details

Licence: Public Domain Mark

Credit: Arithmetica universalis : sive de compositione et resolutione arithmetica liber / Auctore Is. Newton. [Anon]. Source: Wellcome Collection.

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    F T . —AXoinXyq—sAHx X^-f AUq^CHq. Eft autem AH = AG + GH, adeoque AHq,. = AG]^2AGH + GH? & fubdu&o utrinque GHa reftat AH^~GHf“AG^f+ 2 AGH,, hoc eft = 2 AG in-* AG + GH, feu = 2 AG x FH, FI atque adeo eft zEAX—AX^—ppj in X>^ 2 AH _ FI XT. 2I I TT v xXy+ 2AG x FH,i.e.= p^X>5— pj|- AH*Xy + 2AGXFI. Q.E.D. *5 t; Lem. III. Iifdem pofitis eft AX ad Xy—AG ut Xy ad 2 BC. Nam-.fi de aqualibus in Lemmate fecundo fub- ducantur • aqualia in Lemmate primo, reftabunt HI 2 FI aqualia 2 CE x AX X?2— -pjj AH x Xy + 2 AXxX y. Ducatur pars utraque in FH,&fier 2 F H x C E x A X aquale H Ix X y q— 2 FI x A H x X> + 2 AI x F H x X y. Eft autem AI~ AH •+- HI, adeoque 2 F Ix A H — 2 F H x A I — 2 FI x AH—2 FH A—2 FHI Sed 2 FI x AFI—2FHA = 2 AHX,& 2 AHI — 2FHI= aHIx A F. Erga zFIxAH — 2 FHx AI = 2 HIx A F, adeoque aFHxCEx AX = HlxXy? — 2 HI x A F x X y- Et inde HI ad FH ut 2CE X AX ad Xyq-2 AF xXy. Sed per conftruftionem HI eft ad FH ut CE ad BC, atque adeo ut 2CEx AX ad 2BC x AX, & proinde 2BCX AX Sc Xy^—2AF x Xy (per Prop. 9. lib. V. Elem.) erunt aqualia. iEqualium vero redtangulorum proportionalia funt latera, A X ad X y — 2 AF, id eft ad X y — A G ut Xy ad2BC. QdLD. LEM.