Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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DE CIRCULI MAGNIT. INVENTA.
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<
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<
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xml:space
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">SIt portio ſemicirculo minor, cui inſcriptum triangulum
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Fig. 4.</
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maximum A B C. </
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<
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xml:space
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">& </
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<
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diameter circuli à quo portio reſecta eſt, B F, centrum E.
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</
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<
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xml:space
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">Oſtendendum eſt primo, portionis A B C ad triangulum in-
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ſcriptum majorem eſſe rationem quam ſeſquitertiam. </
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<
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xml:space
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portionis A B C centrum grav. </
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<
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xml:space
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">punctum G, & </
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<
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xml:space
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in H, ut ſit H D dupla reliquæ H F.</
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<
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<
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<
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xml:space
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quam dupla G B. </
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<
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xml:space
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">Erit major ratio F B ad B D, quam E B
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ad B G. </
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<
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xml:space
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">Et per converſionem rationis, minor B F ad F D,
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quam B E ad E G. </
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<
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xml:space
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(quæ proportio dupla eſt) quam F D ad E G. </
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<
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xml:space
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major eſt quam dupla E G. </
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<
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xml:space
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">Ipſius autem F D duas tertias
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continet H D. </
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<
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xml:space
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">Ergo H D major eſt quam ſeſquitertia E G.
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</
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<
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xml:space
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">Sicut autem H D ad E G, ita eſt portio A B C ad inſcri-
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ptum ſibi triangulum: </
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<
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xml:space
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">hoc enim antehac demonſtravimus in
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Theorematis de Hyperboles Ellipſis & </
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xml:space
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xml:space
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p. 324.</
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Itaque major eſt ratio portionis ad inſcriptum triangulum
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A B C quam ſeſquitertia.</
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<
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xml:space
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">Quod autem ad triangulum A B C portio minorem ha-
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beat rationem quam tripla ſeſquitertia ipſius D F ad diame-
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trum circuli B F unà cum tripla E D, id nunc oſtendemus.
<
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</
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<
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xml:space
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liquæ R D. </
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<
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xml:space
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<
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xml:space
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xml:space
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>
niam poſitum fuit G centrum gravitatis in portione A B C.
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<
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xml:space
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tio, quæ H D ad E G, ut modo dictum fuit; </
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xml:space
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tem ſit ratio H D ad E G, quam H D ad E R: </
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<
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xml:space
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propterea minor quoque portionis ad inſcriptum triangulum
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ratio quam H D ad E R, ſive quam H D quinquies ſum-
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pta ad quintuplam E R. </
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<
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duabus tertiis D F) quinquies ſumpta æquabitur decem ter-
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tiis, hoc eſt, triplæ ſeſquitertiæ D F. </
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tinet E D & </
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<
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tur, æquabitur duplæ B D & </
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duplæ totius E B atque inſuper triplæ E D. </
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<
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