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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xml:space
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">Ex his manifeſtus eſt Orontii Finei error, qui circumfe-
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rentiæ quadrantem æqualem minori duarum proportione me-
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diarum inter inſcripti & </
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<
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dit, circulum vero æqualem quadrato quod fieret à majori.</
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<
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. XII.
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. XV.</
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I inter productam circuli diametrum & </
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<
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ferentiam recta aptetur radio æqualis, & </
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<
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ducta circulum ſecet, occurr atque tangenti circulum
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ad alterum diametri terminum: </
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<
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xml:space
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tem tangentis arcu adjacente abſciſſo majorem.</
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<
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">Eſto deſcriptus circulus centro C, cujus diameter A B.
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<
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Fig. 7.</
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Hæc autem producatur verſus A, interque ipſam & </
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cumferentiam ponatur E D recta radio A C æqualis. </
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<
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">Quæ
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producta ſecet circumferentiam in F, occurratque tangenti
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in G, ei nimirum quæ circulum contingit ad diametri ter-
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minum B. </
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<
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xml:space
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">Dico tangentem B G majorem eſſe arcu B F.
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</
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<
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">Ducatur enim per centrum recta H L parallela E G, quæ
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circumferentiæ occurrat in punctis H, M: </
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in L Et jungatur D H, quæ diametrum ſecet in K. </
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xml:space
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les itaque ſunt trianguli E D K, C H K, quoniam angu-
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los ad K æquales habent, & </
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<
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">angulum E æqualem angulo
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C. </
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<
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">latus E D æquale eſt lateri H C, ſuntque hæc
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latera æqualibus angulis ſubtenſa. </
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xml:space
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">Ergo æquale etiam latus
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D K lateri K H. </
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<
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xml:space
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">Itaque C A ſecat bifariam ipſam D H,
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itemque arcum D A H. </
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<
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xml:space
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">Arcus igitur D H ſive huic æqua-
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lis F M duplus eſt ad arcum A H. </
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<
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xml:space
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">Ipſi autem A H æqua-
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lis eſt arcus M B. </
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<
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xml:space
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A H. </
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<
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xml:space
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">Porro quoniam H K ſinus eſt arcus H A, ejuſdem-
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que tangenti æquatur L B, erunt duæ tertiæ H K & </
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<
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L B ſimul majores arcu A H . </
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<
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">Quare ſumptis omnium
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plis erit dupla H K, hoc eſt, H D ſive G L una cum L B
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major arcu A H triplo, hoceſt, arcu F B. </
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<
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totam G B arcu F B majorem eſſe.</
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