Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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GEOMET. VARIA.
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atque A F, F B, hoc eſt x & </
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<
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xml:space
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">Nempe ſi in æquatione
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propoſita pro x ſubſtituatur ubique x + e, & </
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<
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xml:space
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y + {ey/z}, debebit æquatio hinc formata terminos omnes ha-
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bere æquales nihilo; </
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<
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xml:space
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x
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+ [3exx] + 3eex + e
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, + y
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+ [{3ey
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/z}] + {3eey
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/zz} + {e
<
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y
<
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/z
<
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} = 0.
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</
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<
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xml:space
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">- axy - [aey] - [{aeyx/z}] - {aeey/z}</
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</
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<
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<
s
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xml:space
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">In hac autem æquatione conſtat neceſſario terminos prio-
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ris æquationis, ex qua formata eſt, contineri debere, nem-
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pe x
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+ y
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- axy: </
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<
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xml:space
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">qui cum ſint æquales nihilo ex proprie-
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tate curvæ, idcirco his in æquatione deletis, neceſſe eſt etiam
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reliquos nihilo æquari, in quibus ſingulis manifeſtum quoque
<
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eſt vel unum e vel plura reperiri, ideoque omnes per e divi-
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di poſſe. </
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<
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xml:space
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">Qui autem poſt hanc diviſionem non amplius ha-
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bebunt e, eos, neglectis reliquis, ſcio nihilo æquari debe-
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re, quantitatemque lineæ z ſive F E oſtenſuros; </
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<
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xml:space
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">ſi nempe
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B E jam tanquam tangens conſideretur, ideoque F G, ſeu
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e, infinitè parva. </
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<
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xml:space
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">Nam termini in quibus adhuc e ſupereſt,
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etiam quantitates infinite parvas ſive omnino evaneſcentes
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continebunt. </
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<
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">Et his quidem hactenus Fermatianæ regulæ
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origo ac ratio declaratur: </
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<
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">nunc porro oſtendemus quomodo
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eadem ad tantam brevitatem perducta ſit. </
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<
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">Video itaque ex
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æquatione totâ noviſſimâ, tantum eos terminos ſeribi neceſ-
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ſe eſſe quibus ineſt e ſimplex, velut hic 3exx + {3ey
<
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/z} - aey -
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{aeyx/z} = 0. </
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<
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xml:space
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">Qui termini quomodo facili negotio ex datis æqua-
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tionis terminis x
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+ y
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- axy = 0, deſcribi poſſint, dein-
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ceps explicandum. </
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xml:space
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">Et primò quidem apparet 3exx +
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{3ey
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/z} nihil aliud eſſe quam ſecundos terminos cuborum </
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