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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. VIII.</
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<
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xml:space
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">MIhi ſanè videor ( videbor & </
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<
s
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xml:space
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">vobis, opinor ) quod irridebat
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_ſapiensille Scurra, perquam exiguæ Civitati portas ingentes_
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_extrnxiſſe_ Nec enim adhuc aliud quàm ad rem aliquanto propiùs eni-
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timur. </
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<
s
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">ad illam.</
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<
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<
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">I. </
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">Hæcadſumimus. </
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xml:space
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">Si duæ lineæ ( OMO, TMT ) ſeſe con-
<
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<
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note-0241-01
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xml:space
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">Fig. 76,
<
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77.</
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tingant, angulosipſæ comprehendunt ( OMT ) rectilineo quovis an-
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gulo minores. </
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>
<
s
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echoid-s11081
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xml:space
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">Et vice versâ: </
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<
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="
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xml:space
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">Si duæ lineæ ( OMO. </
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<
s
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="
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xml:space
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">TMT ) an-
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gulos contineant quovis rectilineo minores, illæ ſeſe contingent _(_con-
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tingentibus ſaltem æquipollebunt_)_.</
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>
<
s
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="
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</
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<
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<
s
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="
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xml:space
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">Hujus _effati_ rationem jampridem _(_ni fallor_)_ attigimus.</
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>
<
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</
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<
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<
s
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">II. </
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<
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">Hinc; </
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xml:space
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">Si duas lineas OMO, TMT tertia quæpiam linea
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PM P contingat, ipſæ etiam lineæ OMO, TMT ſeſe contin-
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gent.</
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>
<
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</
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<
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<
s
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echoid-s11091
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xml:space
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">Nam quoniam lineæ OMO, PM P ſeſe contingunt, erit angulus
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OM P quovis _rectilineo_ minor. </
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>
<
s
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="
echoid-s11092
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xml:space
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">Item, ob linearum TMT, PMP
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_contractum_, erit _angulus_ TM P quovis etiam _rectilineo_ minor. </
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<
s
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="
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xml:space
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">Erit
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igitur angulus TMO _rectilineo_ quovis minor. </
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<
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xml:space
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">Unde lineæ OMO,
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TMT ſe mutuo contingent.</
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<
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">III. </
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">Tangat recta FA curvam FX in F; </
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<
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">ſitque poſitione data recta
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FE; </
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<
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">ſint item duæ curvæ EY, EZ tales, ut ductâ utcunque rectâ
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<
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">Fig 78.</
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IL ad EF parallelâ ( quæ lineas expoſitas ſecet, ut vides ) ſit ſemper
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intercepta KL æqualis interceptæ I G; </
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<
s
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xml:space
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">etiam curvæ EY, EZ ſeſe
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contingent.</
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<
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</
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<
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<
s
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">Si non tangant, poteſt inter ipſas conſtitui angulus rectilineus, puta
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BEC; </
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<
s
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">hunc utcunque ſecet ad FE parallela I L; </
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<
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">ſumatúrque G H
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= BC, & </
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<
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">connectatur F H; </
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<
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