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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146419ET HYPERBOLÆ QUADRATURA.
SCHOLIUM.
Duæ præcedentes propoſitiones eodem modo demon-
ſtrari poſſunt de duobus quibuſcunque polygonis
complicatis loco polygonorum complicatorum ABIP,
A B D L P; polygonum enim à tangentibus comprehenſum
tot continet æqualia trapezia, quot continet polygonum à
ſubtendentibus comprehenſum æqualia triangula: atque hinc
evidens eſt has polygonorum analogias ita ſe habere in infi-
nitum, ducendo nimirum rectas AN, AK, AG, AC, per
puncta R, T, S, V, & adhuc alia & alia polygona intra &
extra ſemper ſcribendo: notandum nos appellare hanc poly-
gonorum inſcriptionem & circumſcriptionem, inſcriptionem
& circumſcriptionem ſubduplam, ex prædictis patet (ſi po-
natur triangulum A B P = a, & trapezium A B F P = b) tra-
pezium A B I P eſſe vqab & polygonum A B D L P {2ab/a + vqab}:
eodem modo poſito trapezio A B I P = c, & polygono
A B D L P = d, erit polygonum A B E I O P = vqcd & po-
lygonum A B C G K N P = {2cd/c + vqcd,}, ita ut evidens ſit hanc
polygonorum ſeriem eſſe convergentem; atque in infinitum
illam continuando, manifeſtum eſt tandem exhiberi quanti-
tatem ſectori circulari, elliptico vel hyperbolico A B E I O P
æqualem; differentia enim polygonorum complicatorum in
ſeriei continuatione ſemper diminuitur, ita ut omni exhibita
quantitate fieri poſſit minor, ut in ſequentis theorematis
Scholio demonſtrabimus: ſi igitur prædicta polygonorum ſe-
ries terminari poſſet, hoc eſt, ſi inveniretur ultimum illud
polygonum inſcriptum (ſi ita loqui liceat) æquale ultimo
illi polygono circumſcripto, daretur infallibiliter circuli &
hyperbolæ quadratura: ſed quoniam difficile eſt, & in geo-
metria omnino fortaſſe inauditum tales ſeries terminare; præ-
mittendæ ſunt quædam propoſitiones è quibus inveniri poſ-
ſint hujuſmodi aliquot ſerierum terminationes, & tandem

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