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

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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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