Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
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">I. </
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xml:space
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">Fig. 19.</
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deſcenſivum continuo creſcentem) progenita linea per omnes ſui partes
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curva evadet.</
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<
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">‖ Accipiantur enim in ipſa tria quælibet puncta M,
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N, O; </
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<
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">per quæ tranſeant BZ, CZ, DZ ad AZ parallelæ, & </
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puncta M, N ducatur recta MNK. </
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<
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xml:space
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">Et quia recta MN gignitur è
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motu compoſito tranſverſo per BC (vel huic parallelam MG) & </
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deſcendente per AZ, uniformi utroque; </
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<
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">tranſverſus autem per MG
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eſt prorſus idem cum tranſverſo, quo linea propoſita MNO de-
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ſcribitur; </
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<
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">patet velocitatem deſcendentis motûs uniformis rectam MN
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gignentis minorem eſſe velocitate, quam motus itidem deſcendens,
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lineam MNO deſcribens, habet in N (etenim niſi motus hic velo-
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cior jam ſit illo, cùm continuò creſcere ponatur, in toto tempore
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deſcenſus per GN illo tardior fuiſſet, adeóque nunquam eodem tem-
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pore ſpatium æquale tranſegiſſet, nec unà cum eo pertigiſſet ad
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punctum N) ergò motus hîc inæqualis & </
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<
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">increſcens per tempus
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motûs uniformis CD continuatus (quo nempe gignitur linea NO)
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majus ſpatium emetitur, quàm uniformis motus deſcendens, quo
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MN. </
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<
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">ad K protractus deſcribitur, eodem tempore CD; </
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<
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">(liquet
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enim eodem tempore à majore vi creſcente majus ſpatium peragi, quàm
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à minore neutiquam creſcente) quare linea HO major eſt quàm HK;
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</
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<
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">adeóque tria puncta M, N, O non exiſtunt in eadem recta linea; </
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quod cùm tribus quibuſvis lineæ MNO punctis conveniat, abunde
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patet eam eſſe nullibi rectam, ſed per omnes ſui partes incurvatam, & </
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inflexam.</
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<
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">velocitas motûs uniformis deſcen-
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dentis, quo curvæ MNO ſubtenſa quævis (ut MN) deſcribitur,
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exiſtente ſcilicet communi tranſverſo motu uniformi quo ipſa, ejúſque
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arcus fiunt, minor eſt velocitate, quàm motus deſcenſivus increſcens
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habet ad communem utriuſque terminum N.</
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<
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(verſus partes AZ) tota cadit, & </
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<
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MNO.</
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<
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">Nam ſi ſumatur in arcu MO punctum quodvis N, & </
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<
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">Elem. III. 2.
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Apoll. I.
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Seren. I. 8.</
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rectæ MN, NO liquet totam MO intra rectas MN, NO jacere,
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& </
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lineam MNO cadit, quia nuſquam alibi ei occurrit, utì mox oſtenſum.</
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<
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">Hoc accidens de circulo ſpeciatim demonſtrat _Euclides, de ſectionibus_
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conicis Apollenius; </
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.</
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