Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
s
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xml:space
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">Nam ſumpto quovis in recta TS puncto K, & </
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<
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AZ parallelâ; </
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<
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xml:space
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">quoniam verſus partes AT velocitas aſcendentis
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puncti, curvam efficientis, ſemper decreſcit ab M ad O, illi verò
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ex hypotheſi par velocitas puncti rectam MT gignentis haud de-
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creſcit ab M ad K, ſitque tempus MG commune, erit ſpatium
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GO minus quàm GK; </
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<
s
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xml:space
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">unde punctum K erit extra curvam. </
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<
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xml:space
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quia verſus alteras partes, velocitas deſcendentis, quo curva fit, in-
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creſcit ſemper ab M verſus O; </
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<
s
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xml:space
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">æqualis autem ei velocitas, quâ recta
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MS fit, haud creſcit ab M ad K; </
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<
s
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xml:space
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">idémque ſit rurſus tempus MG,
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liquet rectam GO excedere rectam GK; </
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<
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xml:space
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">& </
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<
s
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irco punctum K ſupra
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curvam exiſtere. </
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<
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xml:space
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">Quare mani@eſtum eſt omnia dictæ rectæ puncta
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extra curvam exiſtere; </
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<
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xml:space
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<
s
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">eam proinde curvam contingere:
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</
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<
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<
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<
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">Ex hiſce ſtatim _conſectatur, hujuſmodi curvas ad unum_
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_punctum ab una tantùm recta contingi._</
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<
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</
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<
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xml:space
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">Nam tangere ponatur recta MT curvam AMO ad M; </
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<
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fieri poteſt altera MX etiam tangat. </
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<
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xml:space
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">Ergo eodem tempore, eâdem
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velocitate (illâ ſcilicet, quæ puncti curvam deſcribentis ad contactum
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M acquiſitæ velocitati æquatur) deſcribetur utraque recta XP, TM;
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</
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<
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nt, totum & </
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<
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<
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non tanget altera præter poſitam MT.</
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<
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">‖ _Hanc ſpeciatim de circule_
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_demonſtravit Euclides; </
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">de Sectionibus Conicis Apollonius_, de lineis
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aliis alii. </
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<
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xml:space
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">Exhinc _Lucrum_ emergit haud aſpernandum, quòd eâdem
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operâ _propoſitiones de tangentibus inve ſæ demonſtrantur._ </
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<
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determinetur angulus PMT (vel alter quiſpiam quem recta po-
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ſitione data cum tangente facit ad punctum curvæ deſignatum) aut ſi
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determinetur quantitas rectæ PT (vel ſimilis cujuſpiam alterius à
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">_Eucl. III._ 16,
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17.</
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puncto in data poſitione recta deſignato per tangentem interceptæ)
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eo tangens determinabitur. </
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<
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xml:space
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">Et permutatim, ſi tangens ſitu deter-
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">_Apoll. I._ 32, 33,
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34, 35, 36.</
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minetur, angulorum atque linearum ejuſmodi quantitas indè digno-
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ſcetur. </
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tales propoſitiones inverſas demonſtrandi. </
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<
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<
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ſervatu dignum eſt, quia ſæpe talium inverſarum propoſitionum
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una quàm altera longè promptiùs invenitur, atque faciliùs demon-
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ſtratur. </
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<
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">Cujus obſervationis, niſi longiùs evagari nollem, in promptu
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forent _Specimina_.</
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<
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<
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quibuſvis deſignatis curvæ punctis ad ſe proportionem habere </
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