Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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GEOMET. VARIA.
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dicularibus ad F D E, unam ex Aſymptotis, & </
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ter ſe in ratione A D ad D P, ſi Hyperbola A V ſit æquila-
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tera & </
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<
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">quadratum ejus ad angulum Aſymptῶtωn ſit A D F H;
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</
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<
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<
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jus curvæ poſitâ quadraturâ Hyperboles.</
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<
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">Habet illa adhuc alias notabiles affectiones, quales ſunt,
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quod ſpatium infinitum, inter curvam, Aſymptoton, & </
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<
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A D, ſit æquale {1/4} circuli cujus radius eſt A D: </
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dum infinitum, quod producit hoc ſpatium rotando cir-
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ca Aſymptoton, ſit æquale {1/4} ſphæræ ejuſdem radii; </
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ſuperficies ejus ſolidi infiniti, ſine baſi, ſit æqualis circulo, cujus
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radius eſt diagonalis quadrati ex A D.</
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<
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">Non autem propter ea qua huc uſque propoſui de hac cur-
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va hic egi, ſed quia ſimplici Machinâ deſcribi poteſt, quo
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reducitur Hyperbola ad quadratum, quod mihi viſum eſt Geo-
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metrarum conſideratione dignum.</
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">Conſtructio Machinæ nititur in dictâ Tangentis proprieta-
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te & </
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">ſcilicet, ſi in plano horizon-
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tali detur punctum, quod ſuo pondere vel alio modo ali-
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quantulum reſiſtit, junctum extremitati fili vel vectis inflexi-
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lis, cujus altera extremitas movetur, punctum illud deſcri-
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bet curvam, cujus Tangens ſemper erit filum vel vectis. </
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<
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inſtrumento vel machinâ, de qua dixi, movenda eſt extremitas
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D fili vel vectis D A juxta lineam rectam D N, & </
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cuſpis in extremitate altera A hærens erecta maneat dum in-
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terim premetur in planum horizontale, potius elaterio quam
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pondere, quoniam ſic curva A K deſcribitur ſine errore ſen-
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ſibili, licet planum non ſit exacte horizontale; </
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tur, an habeat veram figuram reducendo extremitatem vectis
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N per eandem rectam N D; </
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regrediatur ex K in A, per eandem viam.</
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acurata poſſet haberi pro Geometricâ, eodem modo ut </
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