Huygens, Christiaan - Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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77365DE CIRCULI MAGNIT. INVENTA. benti duplam C G, hoc eſt, C D, & altitudinem C A: tri-
angulum vero A E C æquale triangulo baſin ipſi E F æqua-
lem habenti & altitudinem dictam A C. Itaque apparet duas
tertias quadrilateri A E G C ſimul cum triente trianguli A E C
æquari triangulo qui baſin habeat compoſitam ex duabus ter-
tiis C D & triente E F, altitudinem vero radii A C. Qua-
re ejuſmodi quoque triangulum majus erit ſectore A E C.
Unde liquet baſin ipſius, hoc eſt, compoſitam ex duabus
tertiis ipſius C D & triente ipſius E F, majorem eſſe arcu
C E. Quod erat demonſtrandum.

Theor. IX. Prop. IX.

OMnis circuli circumferentia minor eſt duabus
tertiis perimetri polygoni æqualium laterum ſibi
inſcripti & triente perimetri polygoni ſimilis circum-
ſcripti.

Eſto Circulus cujus A centrum; & inſcribatur ei polygo-
11TAB. XXXIX.
Fig. 1. num æquilaterum, cujus latus C D: ſimileque aliud cir-
cumſcribatur lateribus ad priora parallelis, quorum unum ſit
E F. Dico circuli totius circumferentiam minorem eſſe dua-
bus tertiis ambitus polygoni C D & triente ambitus polygo-
ni E F. Ducatur namque diameter circuli B G, quæ ſimul
inſcripti polygoni latus C D medium dividat in H, & cir-
cumſcripti latus E F in G, (conſtat autem G fore punctum
contactus lateris E F,) Et ponatur H L æqualis ipſi H G,
& jungantur A C, B C & producantur, occurrátque B C
lateri E F in K, producta autem A C incidet in E angu-
lum polygoni circumſcripti. Quoniam igitur H L æqualis
H G, erit B L dupla ipſius A H: Ideoque ut G A ad A H,
ita G B ad B L. Major autem eſt ratio H B ad B L, quam
G B ad B H; quoniam hætres ſeſe æqualiter excedunt G B,
H B, L B. Itaque major erit ratio G B ad B L, hoc eſt,
G A ad A H, quam duplicata rationis G B ad B H. Sicut
autem G A ad A H, ita eſt E G ad C H; & ſicut G

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Scan	Original
101	383
102	384
103	385
104	386
105
106	386
107
108	387
109
110	389
111	390
112	391
113	392
114	393
115	394
116	395
117	396
118	397
119	398
120
121
122
123	399
124	400
125	401
126	402
127	403
128	404
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