Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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CHRISTIANI HUGENII
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nus triente minoris. </
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<
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xml:id
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xml:space
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">Quare ſi à ſexdecim inſcripti dodecago-
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ni lateribus duo latera inſcripti hexagoni, hoc eſt, diameter
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circuli deducatur, reliqua circuli circumferentiâ minor erit,
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aut ſi ab octo dodecagoni lateribus radius deducatur, reliqua
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minor erit circumferentiæ ſemiſſe. </
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<
s
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echoid-s1319
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xml:space
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">Hoc autem ad conſtructio-
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nem mechanicam utile eſt, quoniam exigua eſt differentia,
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ſicut poſtea oſtendetur.</
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<
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<
s
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echoid-s1321
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xml:space
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">Manifeſtum etiam, in omni arcu qui ſemicircumferen-
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tiâ minor ſit, ſi ad ſubtenſam addatur triens exceſſus quo
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ſubtenſa ſinum ſuperat, compoſitam arcu minorem eſſe.</
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<
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. VIII.
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. VIII.</
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">CIrculo dato, ſi ad diametriterminum contingens
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ducatur, ducatur autem & </
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<
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xml:space
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">ab oppoſito diametri
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termino quæ circumferentiam ſecet occurratque tan-
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genti ductæ: </
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<
s
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xml:space
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">erunt interceptæ tangentis duæ tertiæ
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cum triente ejus quæ ab interſectionis puncto dia-
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metro ad angulos rectos incidet, ſimul arcu abſciſ-
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ſo adjacente majores.</
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<
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">Eſto circulus centro A, diametro B C; </
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">& </
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">ducatur ex C
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">TAB. XXXVIII.
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Fig. 8.</
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recta quæ circulum contingat C D: </
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<
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">huic autem occurrat
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ducta ab altero diametri termino recta B D, quæ circumfe-
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rentiam ſecet in E: </
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<
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xml:space
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ctos. </
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xml:space
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">Dico tangentis interceptæ C D duas tertias ſimul cum
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triente ipſius E F, arcu E C majores eſſe. </
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<
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xml:space
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A E, E C; </
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">& </
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<
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">ducatur tangens circulum in E puncto, quæ
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tangenti C D occurrat in G. </
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<
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xml:space
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">Erit igitur G E ipſi G C æqua-
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lis, itemque D G; </
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<
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xml:space
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">nam ſi centro G circumferentia deſcriba-
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tur quæ tranſeat per puncta C, E, eadem tranſibit quoque
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per D punctum, quoniam angulus C E D rectus eſt. </
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<
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">Oſten-
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ſum autem fuit ſuprà, duas tertias quadrilateri A E G C una
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cum triente trianguli A E C ſimul majores eſſe ſectore A E C .</
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<
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<
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Eſtque quadrilaterum A E G C æquale triangulo baſin </
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