Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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ET HYPERBOLÆ QUADRATURA.
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cogniti A B E, cujus arcus A E etiam innoteſcit, datur radius
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B A: </
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bitur ut in antecedente triangulum ſectori inſcriptum A B E & </
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eidem trapezium circumſcriptum A B E C; </
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<
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">atque ipſe ſector
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datus, eſt ſecunda duarum mediarum arithmeticè continuè
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proportionalium inter triangulum ſibi inſcriptum & </
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circumſcriptum; </
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<
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">proinde datur æquatio inter duplum tra-
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pezii A B E C unà cum triangulo A B E & </
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<
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cogniti A B E, cujus reſolutio manifeſtat valorem quantita-
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tis ignotæ z, hoc eſt ſinum A D: </
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">at dato arcu A E & </
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ſinu, dantur etiam ex vulgata ſectionum angularium doctri-
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na ſinus omnium multiplicium ejuſdem arcus A E; </
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de non latet ſinus arcus in initio propoſiti, cum ſit ad arcum
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A E in data ratione multiplici, quem invenire oportuit.</
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">Invenire quadratum æquale ſpatio hyperbolico con-
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tento à curva hyperbolica, uno aſymptoto & dua-
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bus rectis alteri aſymptoto parallelis; quod
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ſpatium æquale eſt ſectori hyperbolico
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cujus baſis eſt eadem curva.</
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fig. 1.</
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currunt in angulo recto O A K. </
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bolæ ſpatium I L M K, contentum à curva hyperbolica I L,
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aſymptoto K M & </
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A O parallelis. </
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L M 10000000000000, A M 1000000000000, & </
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recta quoque K M 9000000000000, invenire menſuram ſpa-
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tii I L M K. </
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I P, ut compleantur rectangula L N K M, Q I K M; </
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ſtum eſt rectangulum L N K M eſſe 9000000000000000000-
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0000000 & </
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