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
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[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
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[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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70358CHRISTIANI HUGENII anguli E B F. Huic autem triangulo æquantur ſingula A E B,
B F C. Ergo utriuſque ſimul triangulum A B C minus erit
quam quadruplum. Quod erat oſtendendum.
Theor. II. Prop. II.
Si fuerit circuli portio, ſemicirculo minor, & ſu-
per eadem baſi triangulum, cujus latera portio-
nem contingant; ducatur autem quæ contingat por-
tionem in vertice: Hæc à triangulo dicto triangu-
lum abſcindet majus dimidio maximi trianguli in-
tra portionem deſcripti.
Eſto circuli portio ſemicirculo minor A B C, cujus vertex
11TAB. XXXVIII.
Fig. 2. B. Et contingant portionem ad terminos baſis rectæ A E,
C E, quæ conveniant in E: convenient enim quia portio ſe-
micirculo minor eſt. Porro ducatur F G, quæ contingati-
pſam in vertice B; & jungantur A B, B C. Oſtendendum eſt
itaque, triangulum F E G majus eſſe dimidio trianguli
A B C. Conſtat triangula A E C, F E G, item A F B,
B G C æquicruria eſſe, dividique F G ad B bifariam. Utra-
que autem ſimul F E, E G, major eſt quam F G; ergo
E F major quam F B, vel quam F A. Tota igitur A E minor
quam dupla F E. Quare triangulum F E G majus erit quarta
parte trianguli A E C. Sicut autem F A ad A E, ita eſt al-
titudo trianguli A B C ad altitudinem trianguli A E C, &
baſis utrique eadem A C. Ergo, quum F A ſit minor quam
ſubdupla totius A E, erit triangulum A B C minus dimi-
dio triangulo A E C. Hujus vero quarta parte majus erat
triangulum F E G. Ergo triangulum F E G majus dimidio
trianguli A B C. Quod oſtendendum fuit.
Theor. III. Prop. III.
OMnis circuli portio, ſemicirculo minor, ad ma-
ximum triangulum inſcriptum majorem ratio-
nem habet quam ſeſquitertiam.

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