Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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GREGORII à S. VINCENTIO.
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A D C B eſt 8, talium erit dimid. </
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quoniam ut 1 ad 32, ita eſt 8 ad 256. </
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<
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tem ſol. </
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<
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E A P Π eſt ad partem A Π S D ut 256 ad 203; </
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<
s
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dendo pars reliqua E D S Φ ad partem A Π S D, ut 53 ad
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203; </
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<
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">quod erat demonſtr. </
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<
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ſolidum, quod ſuprà diximus fieri ex ductu plani E Ξ S in
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planum E M Λ S, eam habere rationem ad ſolidum ortum ex
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ductu plani S Ξ Σ P in planum S Λ Π P, quam 53 ad 203.</
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<
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">Tandem ad alterum eorum quæ demonſtrare promiſimus
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">TAB. XXXVII.
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Fig. 2.</
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accedamus, repetitâque parte mediâ ſchematis triplicis
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quod ſuprà deſcriptum fuit, oſtendendum ſit; </
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tum ex ductu plani C Θ R in planum C K Δ R, ad ſoli-
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dum ex ductu plani R Θ Γ O in planum R Δ Z O eam ha-
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<
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bere rationem, quam 5 ad 11. </
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C D I, erigatur ad perpendiculum triangulum C K D, & </
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jungatur K I. </
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intelligitur fieri ex ductu trianguli C D I in triangulum C D K.
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</
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<
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">Etenim ſectâ pyramide plano A Z O Γ ſecundum O Γ,
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quod rectum ſit ad baſin C D I, erit ſectio quadratum, id
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eſt, rectangul. </
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">eademque ſe-
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ctio dividet pyramidem bifariam. </
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">Secta item plano E Δ R Θ
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priori parallelo, ſecundùm lineam R Θ, exiſtet inde re-
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ctangulum E R, quale continetur lineis Θ R, R Δ. </
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tet itaque oſtendere, quòd ſolidum K C R E Δ eſt ad ſo-
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lidum Δ Λ Ο Θ Δ, ut 5 ad 11.</
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<
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">Ducatur ſecundùm E Δ planum Δ E B parallelum baſi
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C D I; </
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">abſcindet illud pyramidem B E Δ K ſimilem toti
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pyramidi C I D K, quæque proinde erit ad hanc in tripli-
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cata ratione laterum homologorum B Δ ad C D. </
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<
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cum ſit æqualis ipſi C R, quarta pars eſt lateris C D. </
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que qualium partium pyramis B E Δ K eſt unius, talium
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pyramis C I D K erit 64: </
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lidum K A O C erit 32. </
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eſt unius talium quoque priſma B E R eſt 9; </
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ſin habent communem B E Δ, & </
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