Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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CHRIST. HUGENII
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<
s
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xml:space
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">In curvâ propoſita cujus æquatio x
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+ y
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- axy = 0,
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fiet ſecundum hanc regulam dividenda quantitas 3y
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- axy,
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diviſor verò 3xx - ay; </
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<
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xml:space
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">ideoque z = {3y
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- axy/3xx - ay}, quæ
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eſt longitudo cognita, cum dentur x, y & </
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<
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xml:space
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">a.</
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<
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<
s
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xml:space
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">Eſto item alia curva A B H, cujus æquatio axx - x
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-
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xlink:label
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xlink:href
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">TAB. XLV.
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fig. 3.</
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qqy = 0, poſito ſcilicet a & </
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<
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xml:space
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">q eſſe lineas datas, A F vero
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= x, F B = y. </
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<
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xml:space
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xml:space
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">F E dicatur ut ante,
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z. </
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<
s
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xml:space
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">Hîc fiet ſecundum regulam, dividenda quantitas - qqy;
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</
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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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">unde z = {- qqy/2ax - 3xx} Ubi cum
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dividenda quantitas ſit negata, ſi fuerit etiam diviſor minor
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nihilo, hoc eſt ſi 2a minor quam 3x, erit z ſive fe ſumen-
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da in partem ab A averſam. </
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<
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xml:space
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">Si vero 2a major quam 3x, ſu-
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menda erit F E verſus A, ex præcepto regulæ.</
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<
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</
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<
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">Horum vero rationem, ipſiuſque regulæ & </
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<
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">compendii quò
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<
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xlink:label
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xlink:href
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">TAB. XLV.
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fig. 4.</
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reducta eſt, originem ut explicemus, proponatur ut ante
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curva B C, ad cujus punctum B tangens ducenda ſit.</
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<
s
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">Intelligatur primum recta E B D, quæ non tangat curvam
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ſed eam ſecet in B, atque item in alio puncto D, ipſi B
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proximo; </
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<
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<
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">ab utriſque
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punctis B, D ducantur ad rectam A G, iiſdem angulis in-
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clinatæ B F, D G; </
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<
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<
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xml:space
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">ſit A F = x, F B = y, ſicut antea;
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</
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<
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">ponatur que etiam F G data eſſe, quæ ſit e, quæraturque F E
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= z.</
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<
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">Eſt itaque ſicut E F ad F B, hoc eſt, ſicut z ad y, ita E G,
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hoc eſt, z + e ad G D; </
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<
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<
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xml:space
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in qualibet curva ita ſe habere manifeſtum eſt.</
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<
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nens, ex. </
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<
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+ y
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- xya = 0,
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ubi a rectam longitudine datam, velut A H ſignificabat; </
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patet, cum punctum D in curva ponatur, debere eodem mo-
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do duas A G, G D, hoc eſt x + e & </
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<
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