Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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verò nulla omnino immutanda, id eodem redire liquet cùm
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quantitatem negatam, ſive minorem nihilo, tanquam affir-
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matam conſiderandam ibi dixerimus. </
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<
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xml:space
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">Ut autem ratio obſer-
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vationis ibidem adjectæ, in utram partem linea F E accipien-
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da ſit, intelligatur, repetemus figuram in principio poſitam,
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xml:space
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fig. 5.</
note
>
ubi vidimus A G eſſe x + e, E G vero z + e; </
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xml:space
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+ y + {ey/z}. </
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<
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xml:space
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">Si autem tangens ab altera parte lineæ B F cadere
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intelligatur, velut be, atque hæc primùm curvam ſecare fin-
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gatur, ut ibi factum eſt in d, ducaturque dg parallela bf; </
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<
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xml:space
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">fiet
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ponendo rurſus fg = e, fe = z, ut A g quidem fiat x + e,
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ſed eg erit z - e, unde gd = y - {ey/z}. </
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<
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xml:space
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">Atque hinc porrò fa-
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cile eſt perſpicere æquationem ſecundam, quæ ex propoſita
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æquatione, x
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+ y
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- axy = o deſcribitur, hoc caſu fore
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3exx - {3ey3/z} - aey + {aeyx/z} = o, termini ut nempe qui per
<
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z dividuntur, habeant ſigna contraria iis quæ habebant
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in æquatione deſcripta caſu priori, quæ erat 3exx +
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{3ey
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/z} - aey - {aeyx/z}. </
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<
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xml:space
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">Ex hac verò priori ſequitur, quan-
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do quantitas 3exx - aey, ſive quando 3xx - ay (quæ diviſo-
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rem conſtituit ſecundum regulam) fuerit minor nihilo, ſive ne-
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gata, tunc quantitatem reliquam {3ey
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/z} - {aeyx/z}; </
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3y
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- ayx (quæ quantitatem dividendam ſecundùm regulam
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conſtituit) eſſe affirmatam, aut cum illa eſt affirmata, hanc eſ-
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ſenegatam; </
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xml:space
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">quia omnes ſimul æquationis termini æquantur ni-
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hilo. </
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xml:space
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">At contra ex illa æquatione 3exx - {3ey
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/z} - aey +
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{aeyx/z} = o, ſequitur, quando quantitas 3exx - aey, ſive
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3xx - ay, fuerit negata, tunc reliquam - {3ey
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/z} + </
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