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

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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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[Figure 191]
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[192] Pag. 626.TAB. LI.Fig. 1.F E D V S 30 20 10 C L G R H K P A M Z I O X B
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[193] Fig. 2.L K O R E H N I S D G B C
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[194] Fig. 3.A 16 15 14 13 12 11 10 9 B 8 7 6 5 4 3 2 1
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[195] Fig. 4
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[196] Fig. 5.
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[197] Fig. 6.
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[198] Fig. 1.
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[199] Fig. 2.
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[200] Fig. 3.
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[201] Fig. 4.
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[202] Fig. 5.
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[208] Fig. 11.
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[210] Fig. 13.
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190460VERA CIRCULI
PROP. XXXV. PROBLEMA.
Rectâ per datum punctum in diametro ductâ,
ſemicirculum in ratione data dividere.
Sit ſemicirculus A D G, cujus diameter A G, centrum E,
11TAB. XLIV.
fig. 2. punctum in diametro datum B. ſupponatur factum quod
jubetur; ſitque recta B D ſemicirculum dividens in ratione
data: quoniam datur ſemicirculi menſura & ratio in qua
dividitur, igitur datur ejus portio nempe D B G. Sit recta
B D, z: ex datis rectis B D, B E, E D, innoteſcunt tri-
angula D E B, D E F, D E G: deinde ſit ut D E F una cum
D E G ad D E G ità duplum D E G ad trapezium circum-
ſcriptum D E G H: & poſitis primis terminis convergenti-
bus D E G, D E G H continuetur ſeries convergens poly-
gonorum complicatorum, ſecundum circuli proprietates ſæ-
pius repetitas, donec conveniens fuerit approximationem ad-
hibere ita ut exhibeatur ſector D E G, qui una cum trian-
gulo D B E æquatur portioni D B G cognitæ, cujus æquatio-
nis reſolutio manifeſtat ignotam quantitatem z ſeu rectam
B D: reliqua patent.
Idem problema eodem omnino modo reſolvitur in ellipſe,
hyperbola vel earum ſectore dato.
SCHOLIUM.
Si quis prædictorum problematum mechanicam deſideret
praxim; non difficile erit calculum, approximationem,
& æquationis reſolutionem ſecundum vulgatas Geome-
triæ practicæ regulas quodammodo imitari, multa talia
problemata poſſem hic reſolvere ope analyſios & noſtræ ſe-
ricrum convergentium doctrinæ, quæ antea impoſſibilia æſti-
mabantur: ſed dicet fortè aliquis has reſolutiones non eſſe geo-
metricas; reſpondeo, ſi per geometricum intelligatur

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