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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169442VERA CIRCULI C, G; & ideo terminatio ſeriei A, C, E, nempe Z, major
erit terminatione ſeriei A, C, G, nempè X; at ex Archime-
dis quadratura parabolæ conſtat X æqualem eſſe ipſi C dem-
pto triente exceſſus A ſupra C, & proinde Z eadem major
eſt, quod demonſtrare oportuit.
PROP. XXIV. THEOREMA.
IIsdem poſitis; dico Z ſeu ſe-
11
A B # A B
C D # G H
E F # M N
K L # O P
Z # X
ctorem hyperbolæ minorem eſ-
ſe quam minor duarum mediarum
arithmeticè continuè proportio-
nalium inter A & B. Inter A &
B ſit media arithmetica G, & in-
ter G & B ſit media Arithmetica
H, Item inter G & H ſit media Arithmetica M, & inter M
& H ſit media Arithmetica N: continueturque hæc ſeries con-
vergens A B, G H, M N, O P, in infinitum, ut fiat ejus termi-
natio X. ſatis patet ex prædictis G majorem eſſe quam C;
atque H media arithmetica inter G & B major eſt media har-
monica inter easdem G & B; media autem harmonica inter
G & B; major eſt media harmonica inter C & B, nempe D, quo-
niam G major eſt quam C; & ideo media Arithmetica inter G
& B nempe H major eſt quam D media harmonica inter C & B
eodem modo M media Arithmetica inter G & H major eſt me-
dia geometrica inter eaſdem G & H; & quoniam G eſt ma-
jor quam C & H quam D, media geometrica inter G & H
major eſt quam E media geometrica inter C & D; & proin-
de M major eſt quam E. Deinde N media Arithmetica in-
ter M & H major eſt media harmonica inter easdem; & quo-
niam H major eſt quam D & M quam E, media harmonica
inter M & H major eſt quam F media harmonica inter E &
D; & ideo N eadem F major eſt. eodem modo utramque
ſeriem in infinitum continuando, ſemper demonſtratur ter-
minum quemlibet ſeriei A B, C D, minorem eſſe quam idem
numero terminum ſeriei A B, G H; & igitur terminatio ſe-
riei A B, C D, nempe Z, minor erit terminatione ſeriei A

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