Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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HYPERB. ELLIPS. ET CIRC.
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tertiis rectanguli K F B , id eſt, duabus tertiis
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A F; </
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<
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">ſed idem rectangulum ſub Q F, D H, æquale eſt re-
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ctangulo Q D R, quia ut Q D ad Q F, ita fecimus eſſe
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D H ad D R; </
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<
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xml:space
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">ergo rectangulum Q D R æquale duabus ter-
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tiis quadrati A F, ideoque ut Q D ad A F ita {2/3} A F ad D R
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: </
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<
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xml:space
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">ſed ut Q D ad A F, ſic quoque eſt rectangulum ſub Q
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xlink:label
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xml:space
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">16. lib. 6.
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A F, cui æquale quadrilaterum D A Q C, id eſt, ſector
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D A B C ad A F quadratum; </
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">ſector D A B C ad
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quadratum A F, ut {2/3} A F ad D R. </
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<
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xml:space
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">Porro quoniam E cen-
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trum gravitatis eſt totius ſectoris, & </
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tionis A C B, G vero trianguli A C D, conſtat eſſe, ſicut
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triangulus A C D ad A C B portionem ſive ad triangulum
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A Q C, id eſt, ut D F ad F Q, ita H E ad E G ; </
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Arch. de
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Æquipond.</
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convertendo & </
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D F, ita G H, ad H E. </
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ita H D ad D R, erit quoque per converſionem rationis,
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ut D Q ad D F, ita H D ad H R; </
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xml:space
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G H ad H E; </
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">quare & </
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H D ad H R , hoc eſt, ut D Q ad D F. </
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">Sicut autem D Q ad D F, ita eſt quadrilaterum D A Q C, cui æqualis ſector
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D A B C ad A C D triangulum; </
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">igitur ſector D A B C
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ad A C D triangulum ut G D ad E R: </
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triangulus ad D F quadratum, ut A F ad D F, ſive ut {2/3} A F
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ad {2/3} D F id eſt D G. </
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">Igitur ex æquali in proportione perturbata,
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ſicut ſector D A B C ad quadratum D F, ita {2/3} A F ad E R
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, & </
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<
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">convertendo, quadratum D F ad ſectorem D A B
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ut E R ad {2/3} A F. </
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A F eſſe ad ſectorem D A B C, ut D R ad {2/3} A F; </
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duo ſimul quadrata, D F & </
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D A ad ſectorem D A B C ut duæ ſimul E R & </
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eſt ut tota E D ad {2/3} A F . </
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ad D A B C ſectorem, ſicut linea D A ad arcum A B, quia
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nimirum ſector D A B C æqualis eſt rectangulo, baſin ha-
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benti æqualem arcui A B & </
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D A ad arcum A B, ita E D ad {2/3} A F; </
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arcus A B ad {2/3} A F, ſive arcus A B C ad {2/3} A C, ut D A
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vel B D ad D E.</
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