Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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GEOMETRICA VARIA.
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ram Hyperboles per Jac. </
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<
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">Gregorium in exercitationibus ſuis
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Geometricis, ubi inde deducit ſolutionem problematis lon-
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gitudinum, datis vento & </
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<
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xml:space
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">latitudinum differentiâ, quod novum
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credidit Leibnitius, & </
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<
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">quod à Gregorio traditum tunc tem-
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poris non recordabar. </
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<
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xml:space
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">Leibnitius & </
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<
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xml:space
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">Bernoullius, ut cenſeo,
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pervenerunt ad Catenariæ Conſtructionem ope Curvæ,
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quam poſterior illorum habet in 1
<
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. </
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<
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xml:space
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bet ad ſolvendum hoc Problema; </
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<
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xml:space
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">nam Leibnitius mihi ſcri-
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pſit, ſe etiam ad eandem perveniſſe; </
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<
s
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xml:space
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">Et invenio eandem
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cum illâ de qua ante, cujus æquatio eſt a
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= xxyy -
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aayy, cujus quadratura, ut dixi, dependet à quadraturâ Hy-
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perboles: </
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<
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xml:space
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">licet nondum concipere potuerim, quomodo cal-
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culus illos perduxerit ad hanc lineam. </
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<
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xml:space
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">Sed tranſeo ad meam
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conſtructionem, quæ abſque conſideratione aliûs lineæ
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curvæ, dat puncta Catenariæ per dimenſionem lineæ Pa-
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rabolicæ.</
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">Primum fundamentum totius inquiſitionis reſpectu hujus
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fig. 3.</
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lineæ eſt hoc; </
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">Si habeas catenam compoſitam ex variis pon-
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deribus æqualibus filo appenſis, ut BCDEF ſemper trium
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interſtitiorum ſe mutuo ſequentium duæ lineæ extremæ, ut CD,
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F E continuatæ ſibi mutuo occurrunt in linea IH per-
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pendiculari ad Horizontem, quæ dividit interſtitium me-
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dium in duas partes æquales. </
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<
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">Conſiderando porro catenam ita
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compoſitam à ponderibus connexis ad æquales diſtantias,
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quas ponimus infinite exiguas, & </
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">diſpoſitis, ita, ut inter-
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ſtitium infimum BC ſit horizonti parallelum, ſi ſuper quo-
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vis alio interſtitio concipiamus triangula rectangula CDK,
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D E L, quorum unum latus ſit horizontale, videbimus,
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quod ab infimo initium faciendo anguli DCK, EDL, FEM,
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tales ſint, ut illorum Tangentes æqualiter creſcant, ut nu-
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meri 1, 2, 3, 4, id quod demonſtratu facile eſt ex dicto
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principio, licet forſitan eo non perveniſſemus ſine calculo Al-
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gebraico.</
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<
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">Si porro concipiamus partes æquales catenæ CDEFG ex-
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tenſas in recta horizontali in C O P Q R, & </
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<
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ſione O ductam O S, quæ concurrat cum perpendiculari C </
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