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

Table of figures

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[51] Fig. 6.A C D M B
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[52] Fig. 5.A E N F B L D M C G H I K O
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[Figure 53]
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[Figure 54]
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[55] Pag. 398.TAB. XLI.Fig. 1.S T B R K H Q C N O M A E L D
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[56] Fig. 2.D E F B G H C A
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[57] Fig. 3.F D E G A B C
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[58] Fig. 4.G N B H D K A E C F
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[59] Fig. 8K A F c C E B h H G D d
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[60] Fig. 6.C E D A F B R Q
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[61] Fig. 5.G L B H D O A E C K
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[62] Fig. 7.K F A C D B E H G
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[63] Pag. 404.TAB. XLII.Fig. 1.K F M A C D B L E N G
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[64] Fig. 3.G R D B H F E N A X C M P Q K
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[65] Fig. 2.K A F c S C L E B T G D R d
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[66] Fig. 4.K e G P E m B D f R F S H M C A N L Q n
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[67] Fig. 5.B C R E G A F M Q D O
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[68] Fig. 6.B C H G E A M Q P K D
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[69] Fig. 7.B C E G A M P Q K H D
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[Figure 70]
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[71] Pag. 450.TAB.XLIII.Fig. 4.B A F R P C D E G H I K S L M N O
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[72] Fig. 1.F G I K D L E S T O C N H M V R B Q P A
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[73] Fig. 2.F G I K D L E S T O C N V R B Q P A
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[74] Fig. 5.A C B D E
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[75] Fig. 3.A F G I K D L S T E O C N H M V R B Q P
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[Figure 76]
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[Figure 77]
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[Figure 78]
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[Figure 79]
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[Figure 80]
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166439ET HYPERBOLÆ QUADRATURA. ceſſus K ſupra E major exceſſus H ſupra G; cumque E ma-
jor ſit quam G, manifeſtum eſt K majorem eſſe quam H:
eodem prorſus modo demonſtratur in omni ſerierum A, C,
E; A, C, G, continuatione, terminum quemcunque ſeriei
A, C, E, majorem eſſe quam idem numero terminus ſeriei
A, C, G; & ideo terminatio ſeriei A, C, E, nempe Z ma-
jor erit terminatione ſeriei A, C, G, nempe X, at ex Archi-
medis quadratura parabloæ conſtat X æqualem eſſe ipſi C
una cum triente exceſſus C ſupra A, & proinde Z eadem
major eſt, quod demonſtrare oportuit.
PROP. XXI. THEOREMA.
IIsdem poſitis quæ ſupra; dico Z
11
A B # A B
C D # G H
E F # M N
K L # O P
Z # X
ſeu ſectorem circuli vel ellipſeos
minorem eſſe quam major duarum
mediarum continuè proportionalium
arithmeticè inter A & B. inter A &
B ſit media Arithmetica G, & inter
G & B ſit media Arithmetica H; item
inter G & H ſit media Arithmetica M, & inter M & H ſed me-
dia Arithmetica N; continueturque hæc ſeries convergens A B,
G H, M N, O P, in infinitum, ut fiat ejus terminatio X. ſatis
pater ex prædictis G majorem eſſe quam C, atque H media
Arithmetica inter G & B major eſt media harmonica inter eas-
dem G, B; media autem harmonica inter G & B major eſt quam
D media harmonica inter C & B, quoniam G major eſt quam
C; & ideo media Arithmetica inter G & B, hoc eſt H, major
eſt quam D media harmonica inter C & B. eodem modo M
media arithmetica inter G & H major eſt media geometrica
inter easdem G & H: & quoniam G eſt major quam C, &
H quam D; media geometrica inter G & H major eſt quam
E media geometrica inter C & D; & proinde M major
eſt quam E. deinde N media arithmetica inter M & H ma-
jor eſt media harmonica inter eaſdem, & quoniam H major
eſt quam D & M quam E, media harmonica inter M & H
major eſt quam F media harmonica inter E & D; & ideo

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