Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
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. XI.</
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">R Eliquis utcunque patratis, apponemus iam _quæ ad magnitudinum_
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è _tangentibus_ (ſeu è perpendicularibus ad curvas) _Dimenſiones_
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_eliciendas pertinentia ſe objecerunt Tbeoremata_; </
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<
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xml:space
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">de compluribus utiq;
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</
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<
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">ſelectiora quædam.</
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<
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</
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<
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<
s
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xml:space
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">I Sit curva quæpiam VH (cujus axis VD, applicata HD ad VD
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normalis) item linea φZψ talis, ut ſi à curvæ puncto liberè ſumpto
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<
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xml:space
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">Fig. 122.</
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(putaE) ducatur recta EP ad curvam perpendicularis, & </
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<
s
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xml:space
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">recta EAZ ad
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axem perpenicularis, ſit recta AZ interceptæ AP æqualis; </
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<
s
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xml:space
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">erit _ſpatium_
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ADψφ_æq@ lis ſemiſſi quadr ati_ ex recta DH.</
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<
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</
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<
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<
s
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xml:space
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">Nam ſit angulus HDO ſemirectus; </
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>
<
s
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xml:space
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">& </
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<
s
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xml:space
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">æquiſecetur recta V Din-
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definitè punctis A, B, C; </
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<
s
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xml:space
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">per quæ ducantur rectæ EAZ, FBZ,
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GCZ, ad HD parallelæ; </
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<
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xml:space
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">curvæ occurrentes in E, F, G; </
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<
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">à quibus
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rectæ EIY, FKY, GLY ad VD (vel HO) parallelæ ducantur;
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</
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<
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xml:space
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">quin & </
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<
s
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xml:space
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">rectæ EP, FP, GP, HP curvæ VH perpendiculares ſint; </
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<
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xml:space
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neæ verò ſe interſecent; </
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<
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xml:space
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">ut vides. </
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<
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xml:space
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">Eſtque triangulum HLG ſimile
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triangulo PDH (nam ob indefinitam ſectionem curvula GH pro re-
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ctà haberiporeſt) quare HL. </
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<
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<
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xml:space
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">adeóque HL x DH
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= LG x PD; </
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<
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xml:space
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">hoc eſt HL x HO = DC x Dψ. </
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<
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xml:space
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">Simili monſtra
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bitur diſcurſu, quoniam triangulum GMF triangulo PCG aſſimila-
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tur, fore LK x LY = CB x CZ; </
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<
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xml:space
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">& </
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<
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xml:space
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">ſimiliter KI x KY = BA x
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BZ; </
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<
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xml:space
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">itidem denuò ID x IY = AV x AZ; </
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<
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xml:space
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">unde conſtat triangu-
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lum HDO (quod a rectangulis HL x HO + LK x LY + KI x
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KY + ID x IY mi@mè differt) æqu@i ſoatio VDψφ (quod iti-
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dem à rectangulis DC x Dψ + CB x CZ + BA x BZ + AV
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x AZ minimè differt); </
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<
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xml:space
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">hoc eſt {DHq/2} æquari ſpatio VDψφ.</
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<
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xml:space
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">Longiordiſcurſus apagogicus adhiberi poſſit, at quorſum?</
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