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

Table of figures

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[Figure 1]
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[Figure 2]
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[Figure 3]
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[4] Pag. 324.TAB. XXXIV.Fig. 1.O B E P L S Q M R N A K H G D F C
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[5] Fig. 3.B Q P S O N R M E H K G A F D L C
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[6] Fig. 2.B E A G M C D H R F K L
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[7] Fig. 4.B M L K E A D F H C
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[8] Fig. 5.B B A D C A D C E E
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[9] Fig. 8.K G H M E F B L A D C
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[10] Fig. 6.S E B P D
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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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29326THEOR. DE QUADRAT.
Theorema VIII.
IN ſemicirculo & quolibet circuli ſectore, habet
arcus ad duas tertias rectæ ſibi ſubtenſæ hanc ra-
tionem, quam ſemidiameter ad eam, quæ ex centro
ducitur ad ſectoris centrum gravitatis.
Eſto primùm ſemicirculus A B C, deſcriptus centro D,
11TAB. XXXVI.
Fig. 3. ſectuſque bifariam rectâ B D, in qua centrum gravitatis
ſemicirculi ſit E . Dico arcum A B C eſſe ad duas 22Theor. 4. h. A C, ſicut B D ad D E. Jungantur enim A B, B C. Igi-
tur, ut ſemicirculus ad triangulum A B C, ſic ſunt duæ ter-
tiæ B D ad D E , eſt enim B D æqualis diametro 33Theor. 7. h. nis reliquæ. Verùm etiam ut ſemicirculus, id eſt, ut trian-
gulus habens baſin æqualem arcui A B C & altitudinem B D,
ad A B C triangulum, ita eſt arcus A B C ad A C re-
ctam; ergo ut arcus A B C ad A C, ita ſunt duæ tertiæ
B D ad D E, & permutando, ut arcus A B C ad duas tertias
B D, ita A C ad D E, ſive ita {2/3} A C ad {2/3} D E, unde rur-
ſus permutando, ut arcus A B C ad {2/3} A C, ita {2/3} B D ad {2/3}
D E, ſive ita, B D ad D E.
44TAB. XXXVI.
Fig. 4.
Sit deinde ſector D A B C, ſemicirculo minor, bifariam
ſectus rectâ D B, in qua ſectoris centrum gravitatis ponatur
E punctum, & ducatur ſubtenſa A C. Dico rurſus, arcum
A B C ad duas tertias rectæ A C eam habere rationem,
quam B D ad D E. Jungantur enim A B, B C, & totius
circuli ſit diameter K D B, quæ producatur in Q, ut fiat
Q F, ad B F, ſicut portio A C B ad A B C triangulum,
& jungantur A Q, Q C; erit jam triangulus A Q C portio-
ni A C B æqualis. Ponantur deinde centra gravitatis, G tri-
anguli A C D, & H portionis A C B; & ſicut D Q ad
Q F, ita ſit H D ad D R.
Quia igitur ſicut portio A C B ſive triangulus A Q C ad
triangulum A B C, id eſt, ut Q F ad B F, ita {2/3} K F ad
D H , erit rectangulum ſub Q F, D H, æquale 55Theor. 7. h.

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