Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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rectæ AB partibus delineabunt, pariter ut antehac in ſiguræ planæ
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exemplo commonſtratum eſt; </
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<
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xml:space
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">unde ſi ſuperſicies hoc modo procreatæ
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à plano quolibet ad rectam ſeu genetricem, ſeu directricem (quam
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ubique ſitam Superficiei productæ latus appellare licet) parallelo
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ſecetur, ſectio communis duabus rectis parallelis conſtabit æqualibus
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inter ſe. </
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<
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xml:space
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">De Superficiebus autem ità progenitis obſervatu dignum eſt
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(nec enim planè nudas magnitudinum generationes indigitare, ſed & </
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generales nonnullas ipſarum affectiones è diverſis reſultantes generandi
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modis inſinuare propoſitum eſt nobis) quòd ſi linea directrix recta ſit
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(ut in figura per literam Z diſcriminata) Superficiei productæ partes
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parallelis lineis genetricibus interjectæ reſpectivis directricis lineæ
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partibus ſemper proportionales ſunt (ſuperficies nempe BCCB re-
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ſpectivis rectis BB:) </
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<
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">At ſi linea curva pro directrice habeatur (ut in
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figura Y) non ſemper eveniet, ut interceptæ genetricibus rectis Super-
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ficies interceptis curvæ directricis partibus proportionentur; </
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<
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xml:space
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">at ſaltem
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accidet hoc, cùm recta genetrix AB æqualiter ad curvam BC ubique,
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vel ſecundum omnia ejus puncta inclinatur; </
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<
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xml:space
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">quomodo fit in cylindri
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cujuſcunque, laxè vel ſtrictè dicti, recti ſuperficie; </
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<
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xml:space
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">quia tum recta
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genetrix omnibus curvæ punctis (hoc eſt omnibus eam ad dicta puncta
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">Fig. 6.</
note
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tangentibus, eive ſubtenſis rectis eſt perpendicularis.) </
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">Verum ſi, in
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exemplum, curva BC ponatur arcus circularis, qui dividatur æqualiter
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ad puncta B, non erunt neceſſariò ſuperficies ABBA peripheriis
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æqualibus BB inſiſtentes inter ſe pares, quia (præterquam in caſu
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prædicto cylindri recti) rectæ AB ubique ad puncta B inæqualiter
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inclinantur (unam quamvis inclinationem cum alia conferendo) an-
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gulos nempe cum tangentibus ad B aliis ac aliis, & </
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<
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xml:space
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mæquales efficiunt. </
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<
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xml:space
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">E qua re pendet _inſuperabilis illa difficultas,_
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quacum conflictantur, qui _cylindricas obliquas ſuperſicies conantur_
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_dimetiri, ſen cum Cylinàricis Superficiebus rectis, aliìſve quadantenus_
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_cognitis Superficiebus quoad proportionem comparare._ </
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<
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conſimili pacto ſuperſiciem quamvis planam directo motu ſibi parallelo
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progredi, ſcilicet ut prædicto modo, ſingula ipſius puncta lineas
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rectas deſcribant, inter ſe pares, ac parallelas; </
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<
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xml:space
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">vel ut ejus ſingulæ
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rectæ (id quod indè conſectatur) planas Superficies parallelogrammas
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effingant; </
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<
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xml:space
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">cujuſmodi motu deſcribuntur priſmatica quæque cylindricá-
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que corpora; </
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<
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">illa nimirum ipſa, de quorum Superficiebus mox egimus,
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quibúſque ſimili jure poſſunt adaptari, quæ Superficiebus iſtis oſtendi-
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mus convenire. </
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<
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">Veluti quod parallelis planis interjectæ Superſicies
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ipſorum, & </
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reſpectivis) proportionantur. </
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