Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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HOROLOG. OSCILLATOR.
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ſtabit ab A; </
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<
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xml:space
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">interſectio vero rectarum B D, F E, quæ eſt
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<
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<
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<
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<
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.</
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G, cadet ultra punctum D in recta B D. </
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ipſas B D, F E neceſſe eſt, cum curvæ B F ad partem ca-
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vam inſiſtant rectis angulis.</
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<
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<
s
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xml:space
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">Quanto autem punctum F ipſi B propinquius fuerit, tanto
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propius quoque puncta D, G & </
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<
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<
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xml:space
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que, ſi interſtitium B F infinite parvum intelligatur, tria
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dicta puncta pro uno eodemque erunt habenda; </
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<
s
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xml:space
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">ac præterea,
<
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ductâ rectâ B H, quæ curvam in B tangat, eadem quoque
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pro tangente in F cenſebitur. </
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<
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xml:space
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in hanc perpendiculares cadant B K, F L: </
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xml:space
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rectam B O in P, & </
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xml:space
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rectæ, B D, F E, occurrant ipſi K L. </
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<
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xml:space
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">Quia igitur ratio
<
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B G ad G M eſt eadem quæ B O ad M N, data hac dabi-
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tur & </
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<
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">illa; </
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<
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xml:space
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<
s
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xml:space
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">quia recta B M datur magnitudine ac po-
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ſitione, dabitur & </
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<
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xml:space
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in curva C D E, quia G & </
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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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">Datur autem ratio B O ad M N, ſimpliciter quidem in
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Cycloide, ubi primùm omnium illam inveſtigavimus, inve-
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nimuſque duplam; </
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<
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xml:space
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">in aliis vero curvis, quas hactenus exa-
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minavimus, per duarum datarum rationum compoſitionem. </
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<
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<
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Nam quia ratio B O ad M N componitur ex rationibus B O
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ad B P, ſive N H ad L H, & </
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<
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patet, ſi rationes hæ utræque dentur etiam ex iis compoſi-
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tam rationem B O ad M N datum iri. </
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<
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xml:space
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">Illas vero dari in o-
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mnibus curvis geometricis, in ſequentibus patebit; </
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<
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de iis ſemper curvas adſignari poſſe, quarum evolutione de-
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ſcribantur, quæque ideo ad rectas lineas ſint reducibiles.</
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</
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<
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">Ponatur primò parabola eſſe A B F, cujus vertex A,
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">TAB. XVI.
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Fig. 2.</
note
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axis A Q. </
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angulos rectos; </
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res B K, F L; </
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">erunt, ex proprietate parabolæ, ſingulæ
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M K, N L dimidio lateri recto æquales; </
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<
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ni L M, æquales inter ſe K L, M N. </
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<
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B G ad G M componatur ex rationibus N H ad H L, & </
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K L ad M N, uti dictum fuit, ſitque earum poſterior </
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