Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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tervallum IK minus ipſo KL ; </
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<
s
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ptis ipſis MN, NO ; </
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<
s
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xml:space
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<
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<
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<
s
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aliter, opinor, elegantius quam ex adjunctis uno, vel altero Theore-
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<
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xml:space
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mate conſtabit.</
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<
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<
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<
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<
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<
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<
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<
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<
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que diametro ZB conſtituatur ſemicirculus; </
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<
s
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xml:space
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">cui à puncto B adapte-
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tur BD = BA ; </
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<
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<
s
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xml:space
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">per puncta Z, D ducta recta refringenti occur-
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rat in Y ; </
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<
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xml:space
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">tum ad ſemiaxes BZ, BY (centro nempe B, vertice Z) de-
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ſcribatur Hyperbole HZG; </
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<
s
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xml:space
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">in hac autem ſumpto quolibet puncto S
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ducantur SN ad AB, & </
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<
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<
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xml:space
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<
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A N, KN _a_ erit KM _a_ incidentis AN refractus.</
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<
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<
s
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xml:space
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">Nam ex _Hyperbolæ_ natura eſt KBq - ZBq. </
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<
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<
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xml:space
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</
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<
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xml:space
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<
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xml:space
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<
s
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<
s
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xml:space
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<
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<
s
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">quare
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componendo KBq - ZBq + BNq. </
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<
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<
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xml:space
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<
s
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">ABq hoc
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eſt KNq - ZBq. </
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<
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<
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xml:space
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<
s
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">ABq. </
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<
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xml:space
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">permutandóque KNq
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- ZBq. </
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<
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<
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<
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">ABq rurſuſque componendo KNq. </
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<
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ZBq :</
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<
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<
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<
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<
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<
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ZBq. </
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<
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<
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<
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<
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">quare KN. </
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<
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<
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<
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<
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ſius AN reſractus erit: </
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<
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<
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<
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diſtant intervallis ordinatim applicatarum ad _Hyperbolam_, puta recta-
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rum, BZ, MR, NS, OT ; </
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<
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<
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rò (ceu paſſim notum, & </
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<
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hujuſmodi curvas oſtenſum eſt) in majori ratione creſcunt, quam ipſæ
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BM, BN, BO ; </
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<
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<
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<
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<
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<
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<
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<
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</
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<
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<
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">quare ſatìs liquet propoſitum. </
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<
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">Enimverò prope verticem Z
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ordinatarum differentiæ perquam exiguæ ſunt; </
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<
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xml:space
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perpendiculari AB adjacentium radiorum refracti velut è puncto
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Z manare videantur ; </
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<
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<
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<
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xml:space
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">Haud abſimiliter, in ſecundo caſu, ſuper ipſa AB deſcriba-
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tur ſemicirculus; </
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<
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<
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">huic accommodetur BD = BZ; </
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<
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<
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protractáque AD refringenti occurrat ad Y ; </
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<
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xml:space
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bus BZ, BY deſcribatur ellipſis HZG; </
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<
s
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xml:space
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<
s
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">in hac accepto quocunque
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<
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puncto S ducantur SN ad ZB, & </
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<
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<
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tur denique rectæ AN , KN; </
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<
s
xml:id
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</
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<
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xml:space
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">Etenim ex ellipſis natura eſt KSq. </
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<
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<
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<
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:</
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<
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<
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<
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<
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<
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<
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<
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<
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