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

Table of figures

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[11] Fig. 7.E S D P B
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[12] Pag. 326.TAB. XXXV.Fig. 1.N H T Z Ψ G K X S Σ Α E Ξ Y F O L B Δ R P V C Q Ω D M
Page: 31
[13] Fig. 5.B L A C D F M G K E H
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[14] Fig. 4.B L A C D F M G K H E
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[15] Fig. 2.B Δ P R V C Q Ω D A L F O Y Ξ Α Σ X S G K Ψ Z T H E N M
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[16] Fig. 3.B Δ P R V A D Ω Q C L F O Y Ξ Α Σ X S G K E Ψ Z T H E N M
Page: 31
[17] Pag. 328.Fig. 2.B L F A D C H E
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[18] Fig. 1.B L F A D C H E
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[19] Fig. 3.B E A D C
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[20] Fig. 4.Q B H A F C E G R D K
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[21] Fig. 5.B E D A C G F
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[Figure 22]
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[23] Pag. 340.TAB. XXXVII.Fig. 1.C G H F E DH A X Q Y T N V B G
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[24] Fig. 3.γ A F D X B P N V E Q C
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[25] Fig. 2.K C Δ R Θ Z O Γ D I
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[26] Fig. 4.A B D C Π Φ N E S P F
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[27] Fig. 2.M E Ψ Λ Φ S Ξ Π Ρ Σ Ω F L
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[28] Fig. 5.K B Δ E Z A C R O D Θ Γ I
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[Figure 29]
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[Figure 30]
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[Figure 31]
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[32] Pag. 366.TAB.XXXVIII.Fig. 1.B E F G A D C
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[33] Fig. 2.E F G B A C
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[34] Fig. 3.B E D C A F
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[35] Fig. 4.D G E F I B K M N H L A C
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[36] Fig. 5.HD A B C
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[37] Fig. 6.E D C B F G A
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[38] Fig. 8.D E G B A F C
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[39] Fig. 7.N G H I KE L M A P C O F B D
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[40] Pag. 376.TAB. XXXIXFig. 1.E K C B A L H G D F
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18318THEOR. DE QUADRAT.
Quoniam igitur F H, L K ſunt diametro B D parallelæ,
ſuntque D F, D L æquales, oportet lineam H K, quæ duas
F H, L K conjungit, à diametro B D bifariam ſecari; qua-
re eadem H K parallela erit baſi A C , & E H K G 115. lib. 2.
con. linea. Itaque E C parallelogrammum eſt; cujus oppoſita la-
tera quum bifariam dividat diameter B D, erit in ea paral-
lelogrammi centrum gravitatis . Eâdem ratione 229. lib. 1.
Arch. de
Æquipond. gramma erunt H M, N O, P Q, & ſingulorum centra gra-
vitatis in linea B D. Ergo & figuræ ex omnibus dictis pa-
rallelogrammis compoſitæ centrum gravitatis in eadem B D
reperiri neceſſe eſt. Iſta autem figura eadem eſt quæ portio-
ni ordinatè fuerat circumſcripta. Ergo figuræ portioni ordi-
natè circumſcriptæ centrum gravitatis conſtat eſſe in B D por-
tionis diametro. Quod erat oſtendendum.
Theorema IV.
POrtionis hyperboles, ellipſis & circuli, centrum
gravitatis eſt in portionis diametro.
Eſto portio hyperboles, vel ellipſis vel circuli dimidiâ pri-
33TAB. XXXIV.
Fig. 4. mum figurâ non major, A B C; diameter ejus B D. O-
ſtendendum eſt, in B D reperiri portionis A B C gravitatis
centrum.
Si enim fieri poteſt, ſit extra diametrum in E, & ducatur
E H diametro B D parallela. Dividendo itaque D C conti-
nuè bifariam, relinquetur tandem linea minor quam D H;
ſit ea D F, & circumſcribatur portioni figura ordinatè ex
parallelogrammis quorum baſes æquales ſint lineæ D F, &
jungantur B A, B C. Figuræ itaque portioni circumſcri-
ptæ centrum gravitatis eſt in B D portionis diametro. Sit hoc
K, & jungatur E K, producaturque, & occurrat ei A L
parallela B D. Quia autem portio major eſt triangulo A B C,
& exceſſus quo figura circumſcripta portionem ſuperat, mi-
nor parallelogrammo B F, uti ſupra demonſtratum fuit ; 44Theor. 1. erit major ratio portionis A B C ad dictum exceſſum, quàm
trianguli A B C ad B F parallelogrammum, id eſt

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