Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
"/>
per arcum S V. </
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<
s
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xml:space
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">Eadem vero & </
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<
s
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xml:space
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">longiora eſſent, ut nunc
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<
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<
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.</
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oſtendemus.</
s
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<
s
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echoid-s1917
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</
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<
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<
s
xml:id
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echoid-s1918
"
xml:space
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">Eſt enim tempus dictum per tangentem S Λ, cum cele-
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ritate æquabili ex B S, ad tempus per rectam O K cum ce-
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leritate æquabili dimidia ex B Θ, ſicut tangens ſemicirculi
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θ Δ ad rectam P Q . </
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>
<
s
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xml:space
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">ſimiliterque tempus per
<
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xml:space
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">Prop.
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præced.</
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Τ Ξ, cum celeritate æquabili ex B T, eſt ad tempus per
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rectam Κ Ψ cum celeritate æquabili dimidia ex B Θ, ut tan-
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gens Γ Σ ad rectam Q Π. </
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>
<
s
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xml:space
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">Atque ita deinceps ſingula tem-
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pora per tangentes cycloidis, quæ ſunt eadem ſupra dictis,
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erunt ad tempora motus æquabilis per partes ſibi reſponden-
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tes rectæ O Ω, cum celeritate dimidia ex B Θ, ut tangen-
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tes circumferentiæ θ η, iisdem parallelis incluſæ, ad partes
<
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rectæ P ζ ipſis reſpondentes. </
s
>
<
s
xml:id
="
echoid-s1921
"
xml:space
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preserve
">Unde, ut in priori parte de-
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monſtrationis, concludetur omnes ſimul rectas P Q, Q Π
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&</
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<
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">c. </
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<
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xml:space
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">hoc eſt, totam P ζ eſſe ad omnes ſimul tangentes θ Δ,
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Γ Σ, &</
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>
<
s
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">c. </
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>
<
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="
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xml:space
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">ſicut tempus quo percurritur tota O Ω, cum ce-
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leritate dimidia ex B Θ, ad tempora omnia motuum quales
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diximus per tangentes cycloidis S Λ, T Ξ, &</
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<
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">c. </
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<
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">Quare & </
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convertendo, tempora omnia per tangentes cycloidis, eam
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rationem habebunt ad tempus dictum motus æquabilis per
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rectam Ο Ω, ſive per B I, quam dictæ tangentes omnes ar-
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cus θ η ad rectam P ζ vel F G, ac proinde majorem quam
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arcus L H ad rectam F G; </
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<
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xml:space
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">eſt enim arcus θ H, adeoque
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<
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xml:space
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">Prop. 20.
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huj.</
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etiam omnino arcus L H, minor dictis tangentibus arcus θ η .</
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>
<
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="
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xml:space
="
preserve
"> Sed tempus per N M poſuimus ab initio ad idem tempus per
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B I ſe habere ut arcus L H ad rectam F G. </
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>
<
s
xml:id
="
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xml:space
="
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">Ergo tempus per
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N M, multoque magis tempus per S V, minuserit tempore
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per tangentes cycloidis. </
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>
<
s
xml:id
="
echoid-s1932
"
xml:space
="
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">Quod eſt abſurdum, cum hoc tempus,
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illo per arcum S V, antea minus oſtenſum fuerit. </
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>
<
s
xml:id
="
echoid-s1933
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xml:space
="
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">Patet igi-
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tur tempus per arcum cycloidis B E ad tempus per tangen-
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tem B I cum celeritare æquabili dimidia ex B Θ, non mi-
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norem rationem habere quam arcus F H ad rectam F G.
<
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</
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>
<
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="
echoid-s1934
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="
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">Sed nec majorem habere oſtenſum fuit. </
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>
<
s
xml:id
="
echoid-s1935
"
xml:space
="
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">Ergo eandem habeat
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neceſſe eſt. </
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>
<
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">quod erat demonſtrandum.</
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>
<
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="
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