Barrow, Isaac - Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

[31.] Lect. IV.

Page: 222 (29)

[32.] Lect. VII.

[33.] Lect. VIII.

[34.] Lect. IX.

[35.] Lect. X.

[36.] Exemp. I.

[37.] _Exemp_. II.

[38.] _Exemp_. III

[39.] Exemp. IV.

[40.] Eæemp. V.

[41.] Lect. XI.

[42.] APPENDICUL A.

[43.] Lect. XII.

[44.] APPENDICULA 1.

[45.] Præparatio Communis.

Page: 303 (110)

[46.] APPENDICULA 2.

Page: 308 (115)

[47.] Conicorum Superſicies dimetiendi Metbodus.

[48.] Exemplum.

[49.] Prop. 1.

[50.] Prop. 2.

[51.] Prop. 3.

[52.] Prop. 4.

[53.] APPENDICULA 3.

[54.] Problema I.

[55.] Exemp. I.

[56.] Exemp. II.

[57.] Probl. II.

[58.] Exemp. I.

[59.] _Exemp_. II.

[60.] _Probl_. III.

27885

Lect. XI.

R Eliquis utcunque patratis, apponemus iam _quæ ad magnitudinum_
è _tangentibus_ (ſeu è perpendicularibus ad curvas) _Dimenſiones_
_eliciendas pertinentia ſe objecerunt Tbeoremata_; de compluribus utiq;
ſelectiora quædam.

I Sit curva quæpiam VH (cujus axis VD, applicata HD ad VD
normalis) item linea φZψ talis, ut ſi à curvæ puncto liberè ſumpto
11Fig. 122. (putaE) ducatur recta EP ad curvam perpendicularis, & recta EAZ ad
axem perpenicularis, ſit recta AZ interceptæ AP æqualis; erit _ſpatium_
ADψφ_æq@ lis ſemiſſi quadr ati_ ex recta DH.

Nam ſit angulus HDO ſemirectus; & æquiſecetur recta V Din-
definitè punctis A, B, C; per quæ ducantur rectæ EAZ, FBZ,
GCZ, ad HD parallelæ; curvæ occurrentes in E, F, G; à quibus
rectæ EIY, FKY, GLY ad VD (vel HO) parallelæ ducantur;
quin & rectæ EP, FP, GP, HP curvæ VH perpendiculares ſint; li-
neæ verò ſe interſecent; ut vides. Eſtque triangulum HLG ſimile
triangulo PDH (nam ob indefinitam ſectionem curvula GH pro re-
ctà haberiporeſt) quare HL. LG: : PD. DH. adeóque HL x DH
= LG x PD; hoc eſt HL x HO = DC x Dψ. Simili monſtra
bitur diſcurſu, quoniam triangulum GMF triangulo PCG aſſimila-
tur, fore LK x LY = CB x CZ; & ſimiliter KI x KY = BA x
BZ; itidem denuò ID x IY = AV x AZ; unde conſtat triangu-
lum HDO (quod a rectangulis HL x HO + LK x LY + KI x
KY + ID x IY mi@mè differt) æqu@i ſoatio VDψφ (quod iti-
dem à rectangulis DC x Dψ + CB x CZ + BA x BZ + AV
x AZ minimè differt); hoc eſt {DHq/2} æquari ſpatio VDψφ.

Longiordiſcurſus apagogicus adhiberi poſſit, at quorſum?

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