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

Table of figures

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[41] Fig. 2.D B G H C E F
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[42] Fig. 4.E C G A F B D
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[43] Fig. 3.E C D F G H I
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[44] Fig. 5.B F R C P L M O
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[45] Fig. 6.Y S H E K B C G F R A L D N P M Z X V T
Page: 93
[46] Fig. 7.G F D M L E A K C B H
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[47] Pag. 386.TAB. XL.Fig. 2.K B H F G E A I D L C
Page: 106
[48] Fig. 1.L K E D H C A G B
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[49] Fig. 3.B Q N L M F G S H K A D C P
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[50] Fig. 4.B G R A C D E H F
Page: 106
[51] Fig. 6.A C D M B
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[52] Fig. 5.A E N F B L D M C G H I K O
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[Figure 53]
Page: 108
[Figure 54]
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[55] Pag. 398.TAB. XLI.Fig. 1.S T B R K H Q C N O M A E L D
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[56] Fig. 2.D E F B G H C A
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[57] Fig. 3.F D E G A B C
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[58] Fig. 4.G N B H D K A E C F
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[59] Fig. 8K A F c C E B h H G D d
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[60] Fig. 6.C E D A F B R Q
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[61] Fig. 5.G L B H D O A E C K
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[62] Fig. 7.K F A C D B E H G
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[63] Pag. 404.TAB. XLII.Fig. 1.K F M A C D B L E N G
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[64] Fig. 3.G R D B H F E N A X C M P Q K
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[65] Fig. 2.K A F c S C L E B T G D R d
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[66] Fig. 4.K e G P E m B D f R F S H M C A N L Q n
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[67] Fig. 5.B C R E G A F M Q D O
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[68] Fig. 6.B C H G E A M Q P K D
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[69] Fig. 7.B C E G A M P Q K H D
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[Figure 70]
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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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