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

Table of figures

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[41] Fig. 2.D B G H C E F
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[42] Fig. 4.E C G A F B D
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[43] Fig. 3.E C D F G H I
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[44] Fig. 5.B F R C P L M O
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[45] Fig. 6.Y S H E K B C G F R A L D N P M Z X V T
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[46] Fig. 7.G F D M L E A K C B H
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[47] Pag. 386.TAB. XL.Fig. 2.K B H F G E A I D L C
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[48] Fig. 1.L K E D H C A G B
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[49] Fig. 3.B Q N L M F G S H K A D C P
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[50] Fig. 4.B G R A C D E H F
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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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150423ET HYPERBOLÆ QUADRATURA. quos terminos æquales appellamus ſeriei terminatio-
nem.
PROP. VII. PROBLEMA.
Oportet prædictæ ſeriei terminationem
invenire.
Ut huic problemati ſatisfiat, oportet primò invenire
quantitatem quæ eodem modo componitur ex termi-
nis convergentibus a, b, quo ex terminis convergentibus
{ca + bd - ad/c}, {bc - bc + ae/c}, hoc autem facile fit hoc modo: inveniatur
quantitas quæ multiplicata in a & addita b multiplicata in
quantitatem data m, eandem quantitatem facit ac ſi multi-
plicaretur in {ca + bd - ad/c} & adderetur {bc - be + ae/c} multiplicata etiam
in eandem quantitatem data\m m. ſit quantitas illa z, & pro-
inde za + bm æquatur {zca + zbd - zad + mbe - mbe + mae/c}, & æquatione
reducta invenitur {z = mac - mbe/ad - bd}; quæ quantitas ſive multiplica-
ta in a & addita m, ſive multiplicata in {ca + bd - ad/c} & addita
{mbe - mbe + mae/c} efficit eandem in utroque caſu quantitatem nempe
{maae - mbae + mbad - mbbd/cd - bd}: & proinde prædicta quantitas eodem mo-
do componitur ex terminis convergentibus a, b, quo compo-
nitur ex terminis convergentibus {ca + bd - ad/c}, {bc - be + ae/c}. atque a
& b quoniam ſunt quantitates indefinitæ poſſunt eſſe quili-
bet totius ſeriei termini convergentes, modò termini con-
vergentes immediatè ſequentes ſint {ca + bd - ad/c} & {bc - be + ae/c}, &
proinde quantitas {maae - mbae + mbad - mbbd/cd - bd} eodem modo componi-
tur ex quibuslibet totius ſeriei terminis convergentibus quo
componitur ex terminis convergentibus a, b; & igitur

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