Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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portionalis linea H. </
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<
s
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xml:space
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">Erit hæc radius circuli qui ſuperficiei
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<
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<
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.</
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ſphæroidis propoſiti æqualis ſit.</
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<
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style
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xml:space
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">Conoidis hyperbolici ſuperficiei curvæ circulum
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æqualem invenire.</
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<
s
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echoid-s2324
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xml:space
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">ESto conoides hyperbolicum cujus axis A B, ſectio per
<
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<
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xlink:label
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xml:space
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">TAB. XIV.
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Fig. 4.</
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axem hyperbola C A D, cujus latus tranſverſum E A,
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centrum F, latus rectum A G.</
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<
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<
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<
s
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xml:space
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">Sumatur in axe recta A H, æqualis dimidio lateri recto
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A G. </
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<
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">& </
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<
s
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xml:space
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">ut H F ad A F longitudine ita, ſit A F ad F K
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potentiâ. </
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<
s
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xml:space
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">Et intelligatur vertice K alia hyperbola deſcripta
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K L M, eodem axe & </
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<
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xml:space
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">centro F cum priore, quæque late-
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ra rectum & </
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<
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">transverſum illi reciproce proportionalia habeat.
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</
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<
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xml:space
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">Occurrat autem ipſi producta B C in M, ſitque A L paralle-
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la B C. </
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<
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xml:space
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">Erit jam ſicut ſpatium A L M B, tribus rectis lineis
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& </
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<
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xml:space
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">curva hyperbolica comprehenſum, ad dimidium quadra-
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tum ex B C, ita ſuperficies conoidis curva ad circulum ba-
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ſeos ſuæ, cujus diameter C D. </
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<
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">Unde conſtructio reliqua
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facile abſolvetur, poſitâ hyperbolæ quadraturâ.</
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<
s
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xml:space
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">Quum igitur conoidis parabolici ſuperficies ad circulum
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redigatur, æque ac ſuperficies ſphæræ, ex notis geometriæ
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regulis; </
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<
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xml:space
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">in ſuperficie ſphæroidis oblongi, ut idem fiat, po-
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nendum eſt arcus circumferentiæ longitudinem æquari poſſe
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lineæ rectæ. </
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<
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xml:space
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">Ad ſphæroidis vero lati, itemque ad conoidis
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hyperbolici ſuperficiem eadem ratione complanandam, hy-
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perbolæ quadratura requiritur. </
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<
s
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xml:space
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">Nam parabolicæ lineæ lon-
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gitudo, quam in ſphæroide hoc adhibuimus, pendet à qua-
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dratura hyperbolæ, ut mox oſtendemus.</
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<
s
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xml:space
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">Verum, quod non indignum animadverſione videtur, in-
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venimus absque ulla hyperbolicæ quadraturæ ſuppoſitione,
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circulum æqualem conſtrui ſuperficiei utrique ſimul, ſphæ-
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roidis lati & </
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<
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xml:space
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">conoidis hyperbolici.</
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<
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<
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xml:space
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">Dato enim ſphæroide quovis lato, poſſe inveniri conoi-
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des hyperbolicum, vel contra, dato conoide hyperbolico,
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poſſe inveniri ſphæroides latum ejusmodi, ut utriusque </
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