Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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æqualitatis; </
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<
s
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xml:space
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">liquet rationem B G ad G M fore eandem quæ N H
<
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<
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<
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<
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<
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<
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ad H L; </
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<
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xml:space
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">& </
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<
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xml:space
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">dividendo, B M ad M G, eandem quæ N L
<
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ad L H, ſive M K ad K H; </
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<
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xml:space
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">nam L H, K H pro eadem
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habentur, propter propinquitatem punctorum B, F. </
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<
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xml:space
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">Data
<
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autem eſt ratio M K ad K H, dato puncto B; </
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<
s
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xml:space
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<
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tam M K, quam K H dantur magnitudine; </
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<
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xml:space
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<
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æquatur dimidio lateri recto, K H vero duplæ K A. </
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<
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xml:space
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">Dataque
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etiam eſt poſitione & </
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<
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xml:space
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">magnitudine recta B M. </
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">Ergo & </
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data erit, adeoque & </
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<
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xml:space
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">punctum G, ſive D, in curva R D E;
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</
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<
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xml:space
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">quod nempe invenitur productâ B M uſque in G, ut ſit
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B M ad M G ſicut {1/2} lateris recti ad duplam K A.</
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<
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</
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<
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<
s
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xml:space
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">Et ſic quidem, adſumptis in parabola A B F aliis quotli-
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bet punctis præter B, totidem quoque puncta lineæ R D E,
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/>
ſimili ratione, invenientur; </
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<
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xml:space
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">atque hoc ipſo lineam R D E
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geometricam eſſe conſtat, unáque proprietas ejus innoteſcit,
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ex qua cæteræ deduci poſſunt. </
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>
<
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xml:id
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xml:space
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">Ut ſi inquirere deinde veli-
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mus, quanam æquatione exprimatur relatio punctorum
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omnium curvæ C D E ad rectam A Q: </
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<
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">ducta in hanc perpen-
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diculari D Q, vocatoque latere recto parabolæ A B F, a;
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</
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<
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<
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xml:space
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">Quoniam ratio B M ad M D,
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hoc eſt, K M ad M Q, eſt ea quæ {1/2} a ad 2 b, eſtque ipſa
<
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K M = {1/2} a, erit & </
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<
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xml:space
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">M Q æqualis 2 b. </
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<
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xml:id
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xml:space
="
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">Eſt autem M A = {1/2}
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a + b. </
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<
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xml:id
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xml:space
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">ergo A Q ſive x æqualis 3 b + {1/2} a. </
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<
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">Unde b = {1/3} x
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-{1/6} a. </
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<
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xml:space
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">Porro quoniam, ſicut quadratum M K, hoc eſt, {1/4} a a
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ad quadratum K B, hoc eſt, a b, ita qu. </
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<
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">M Q, hoc eſt,
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4 b b ad qu. </
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<
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/4}. </
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xml:space
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">Ubi, ſi in
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locum b ſubſtituatur {1/3} x - {1/6}a, quod illi æquale inventum eſt,
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fiet y y = 16. </
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<
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xml:space
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<
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">Ac proinde {27/16} a y y
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= cubo ab x - {1/2} a. </
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<
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xml:space
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">Accipiatur A R in axe parabolæ = {1/2} a; </
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eritque R Q = x - {1/2} a. </
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<
s
xml:id
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xml:space
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">Curvam igitur C D ejus naturæ eſſe
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liquet, ut ſemper cubus lineæ R Q æquetur parallelepipedo,
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cujus baſis qu. </
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<
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<
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xml:space
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">ac proinde ipſam para-
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boloidem eſſe, cujus evolutione deſcribi parabolam A B ſu-
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pra oſtendimus; </
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<
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xml:space
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quetur {27/16} lateris recti parabolæ A B. </
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<
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">tunc enim hujus latus
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rectum æquale fit {15/27} lateris recti paraboloidis, quemadmo-
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dum ibi fuit deſinitum.</
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