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

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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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[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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176449ET HYPERBOLÆ QUADRATURA. cogniti A B E, cujus arcus A E etiam innoteſcit, datur radius
B A: ſit ejus ſinus A D, z; & proinde è dato ſinu & radio, da-
bitur ut in antecedente triangulum ſectori inſcriptum A B E &
eidem trapezium circumſcriptum A B E C; atque ipſe ſector
datus, eſt ſecunda duarum mediarum arithmeticè continuè
proportionalium inter triangulum ſibi inſcriptum & trapezium
circumſcriptum; & proinde datur æquatio inter duplum tra-
pezii A B E C unà cum triangulo A B E & triplum ſectoris
cogniti A B E, cujus reſolutio manifeſtat valorem quantita-
tis ignotæ z, hoc eſt ſinum A D: at dato arcu A E & ejus
ſinu, dantur etiam ex vulgata ſectionum angularium doctri-
na ſinus omnium multiplicium ejuſdem arcus A E; & proin-
de non latet ſinus arcus in initio propoſiti, cum ſit ad arcum
A E in data ratione multiplici, quem invenire oportuit.
PROP. XXXII. PROBLEMA.
Invenire quadratum æquale ſpatio hyperbolico con-
tento à curva hyperbolica, uno aſymptoto & dua-
bus rectis alteri aſymptoto parallelis; quod
ſpatium æquale eſt ſectori hyperbolico
cujus baſis eſt eadem curva.
Sit hyperpola D I L, cujus aſymptota A O, A K, ſibioc-
11TAB. XLIV.
fig. 1. currunt in angulo recto O A K. proponitur hujus hyper-
bolæ ſpatium I L M K, contentum à curva hyperbolica I L,
aſymptoto K M & duabus rectis I K, L M, alteri aſymptoto
A O parallelis. oportet è datis recti I K 10 000000000000,
L M 10000000000000, A M 1000000000000, & proinde
recta quoque K M 9000000000000, invenire menſuram ſpa-
tii I L M K. Producantur rectæ I K, O L, & ducatur recta
I P, ut compleantur rectangula L N K M, Q I K M; manife-
ſtum eſt rectangulum L N K M eſſe 9000000000000000000-
0000000 & Q I K M 9000000000000000000000000 &

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