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

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[161] Fig. 42.* 19. Maii.
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[162] Fig. 43.* 17. Dec.
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[163] Fig. 44.* 18. Dec.
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[164] Fig. 45.* 27. Dec.
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[165] Fig. 46.* 11. Mart 1658.
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[166] Fig. 47.* 16. Mart.
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[167] Fig. 48.* 23. Mart.
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[168] Fig. 49.* 3. Apr.
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[169] Fig. 50.* 10. Nov.
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[170] Fig. 51.* 16. Ian. 1659.
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[171] Fig. 52.12. Febr. *
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[172] Fig. 53.* 24. Febr.
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[173] Fig. 54.25. Febr. *
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[174] Fig. 55.14. Mart. *
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[175] Fig. 56.16. Mart. *
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[176] Fig. 57.* 21. Mart.
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[177] Fig. 58.* 22. Mart.
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[178] Fig. 59.26. Mart. *
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[179] Pag. 574.TAB. XLIX.Fig. 2.
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[180] Fig. 1.C K O B H N G M S * F D A L E
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[181] Fig. 3.E C D A * B
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[182] Fig. 4.P Q O N M L * C R
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[183] Fig. 5.C * V S X T Y
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[184] Fig. 6.
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[185] Fig. 7.
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[186] Pag. 580.TAB. L.Fig. 2.R ♈ L D I T A N ♋ H G E P F K C Q O B M S
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[187] Fig. 3.
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[188] Fig. 4.N Q F C P L E A M H O D f
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[189] Fig. 1.B A
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[Figure 190]
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164437ET HYPERBOLÆ QUADRATURA.
PROP. XVII. THEOREMA.
IIsdem poſitis: dico exceſſum A ſupra C majorem eſſe
quadruplo exceſſus C ſupra E. ex prædictis manifeſtæ
ſunt ſequentes tres analogiæ; prima, quoniam A, C, B, ſunt
continuè proportionales; ſecunda, quoniam C, D, B, ſunt
harmonicè proportionales; & tertia, quoniam C, E, D, ſunt
continuè proportionales; & ideo exceſſus A ſupra C, hoc eſt
A - C, eſt ad exceſſum C ſupra E, hoc eſt C - E in ratio-
ne compoſita ex proportionibus
11
A - C:C: - B::A:C
C - B:C - D::A + :CA
C - D:C - E::E + C:C
A ad C, A + C ad A & E + C ad C;
& ideo A - C eſt ad C - E,
ut A C + E C + A E + CC ad
CC; at B minor eſt quam E,
& ideo AB, ſeu CC minor eſt quam A E; & igitur AE +
CC major eſt quam 2 CC. atque A C + E C eſt ad 2 CC ut
A + E ad 2 C; ſed A + E major eſt quam duo C, & ideo
A C + E C major eſt quam 2 CC; & proinde A C + E C + A E
+ C C major eſt quam 4 CC; & igitur A - C major eſt qua-
druplo ipſius C - E, quod demonſtrare oportuit.
PROP. XVIII. THEOREMA.
SInt duæ quantitates inæquales; A
22
# E
A # C # B
# D
minor, B major, C media geome-
trica, D media arithmetica. dico D
majorem eſſe quam C, quoniam B, C,
A, ſunt continuè proportionales; erit divi-
dendo, permutando, & componendo; ut exceſſus B ſupra A
ad exceſſum C ſupra A, ita A + C ad A, atque A + C major eſt
duplo ipſius A; & proinde exceſſus B ſupra A major eſt duplo
exceſſus C ſupra; ſed exceſſus B ſupra A duplus eſt exceſſus
D ſupra A, & ideo exceſſus D ſupra A major eſt exceſſu

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