Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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ΕΞΕΤΑΣΙΣ CYCLOM.
"/>
in priori. </
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<
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xml:space
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">Sed veritus ne intricata & </
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<
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xml:space
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">prolixa hinc nobis diſ-
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putatio oriretur, ad alias inventiones me converti, & </
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<
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xml:space
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dem ea ſeſe obtulerunt, quæ paucis hic perſcribere conſtitui.
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</
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<
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xml:space
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">Nulla per hæc propoſitionum Cl. </
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<
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xml:space
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">Viri in controverſiam vo-
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cabitur; </
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<
s
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xml:space
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">ſed contrà multis earum probatis, atque in uſum
<
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meum converſis, eò rem deducam, ut ſi quidem non impoſ-
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ſibile dicet quadraturam ſuam ad exitum perducere, & </
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>
<
s
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="
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xml:space
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">per
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eam reapſe invenire rectilineum circulo æquale, oſtendam
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qui id facillimè impoſterum aſſequatur. </
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<
s
xml:id
="
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xml:space
="
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">Deinde veſtigia i-
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pſius inſiſtens demonſtrabo, quibus hactenus nobis præceſſit,
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iis nequaquam ad optatum finem perveniri poſſe, ſed eſſe
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ſubſiſtendum ad concluſiones perquam abſurdas. </
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>
<
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xml:space
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">Atque ut
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ad rem veniamus.</
s
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<
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</
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<
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<
s
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xml:space
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">Eſto circulus cujus centrum F, diameter C D. </
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<
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xml:space
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xml:space
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">TAB. XXXVII.
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Fig. 1.</
note
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radio F C bifariam in G, ducantur ipſi ad angulos rectos
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F E, G H. </
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xml:space
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">Dico, datâ ratione ſegmenti C H G ad G H E F
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ſegmentum, dari quoque rationem circuli ad inſcriptum ſibi
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hexagonum regulare. </
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<
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xml:space
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">Jungantur enim F H, H C, & </
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<
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feſtum eſt triangulum F H C fore æquilaterum; </
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<
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xml:space
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drantis arcum C E triplum fore arcus H E. </
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<
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xml:space
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">Si ergo data ſit
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ratio ſegmenti C H G ad G H E F ſegmentum, componen-
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do quoque, data erit ratio quadrantis F E C ad ſegmentum
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G H E F. </
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xml:space
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">Sed data quoque eſt ratio ſectoris F H E ad qua-
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drantem F E C, ergo datur quoque ratio ſegmenti G H E F
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ad ſectorem F H E; </
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<
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xml:space
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">ac proinde dabitur quoque ratio ſe-
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gmenti G H E F ad triangulum F H G; </
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xml:space
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">quare & </
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<
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">ratio ſe-
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ctoris F H E ad triangulum F H G data erit. </
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<
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xml:space
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">Sed huic ra-
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tioni eadem eſt ratio ſectoris F H C ad triangulum F C H,
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(quoniam hæc utriuſque præcedentium dupla ſunt;) </
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<
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xml:space
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">eadem-
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que eſt circuli ratio ad hexagonum regulare ſibi inſcriptum.
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</
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">hanc datam eſſe apparet: </
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<
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xml:space
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">quod erat demonſtran-
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dum.</
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">TAB. XXXVII.
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Fig. 1. 2.</
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metro circuli C D: </
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<
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xml:space
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bina quadrata. </
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xml:space
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parabolæ A V G, B T H, quarum baſes ſint </
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