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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170443ET HYPERBOLÆ QUADRATURA. G H, nempe X; atque ex hujus 7 terminatio ſeriei A B,
G H, nempe X, æqualis eſt minori duarum mediarum arith-
meticè continuè proportionalium inter A & B, & ideo Z ea-
dem minor eſt, quod demonſtrare oportuit.
PROP. XXV. THEOREMA.
Iisdem poſitis; dico Z ſeu ſectorem
11
A B # A B
C D # G H
E F # M N
K L # O P
Z # X
hyperbolæ minorem eſſe quam mi-
nor duarum mediarum geometricè con-
tinuè proportionalium inter A & B.
Inter A & B ſit media geometrica G,
& inter G & B media geometrica H;
Item inter G & H media geometrica M, & inter M & H media
geometriea N; continueturque hæc ſeries convergens AB, GH,
MN, OP, & c. in infinitum ut fiat ejus terminatio X. ſatis patet
ex prædictis C & G eſſe inter ſe æquales, & H majorem eſſe
quam D; atque ob hanc rationem M media geometrica inter G
& H major eſt quam E media geometrica inter C & D. Deinde
N media geometrica inter M & H major eſt media harmonica
inter eaſdem; & quoniam M major eſt quam E & H quam D, erit
media harmonica inter M & H major quam F media harmo-
nica inter E & D; proinde N media geometrica inter M & H
major eritquam F. eadem methodo utramque ſeriem in in-
finitum continuando, ſemper demonſtratur terminum quem-
libet ſeriei A B, C D, minorem eſſe quam idem numero ter-
minus ſeriei A B, G H; & igitur terminatio ſeriei A B, C D,
nempe Z minor erit quam terminatio ſeriei A B, G H, nem-
pe X; atque ex hujus 9 terminatio ſeriei A B, G H, ſeu X, æqua-
lis eſt minori duarum mediarum geometricè continuè propor-
tionalium inter A & B; & ideo Z eadem minor eſt, quod
demonſtrare oportuit.
Ex dictis manifeſtum eſt hanc approximationem exactio-
rem eſſe illa, in antecedenti propoſitione, demonſtrata, et-
iamſi hæc ſit paulò laborioſior. ſed non diſſimulandum
eſt duas poſſe eſſe ſeries æquales terminationes habentes,

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