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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<
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incidentiæque punctis interjectam partem) minorem quartâ parte
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totius N Π. </
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<
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<
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">HR Π = ang. </
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<
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echoid-s3126
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">N Π R; </
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<
s
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">quapropter
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erit HR = H Π; </
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<
s
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xml:space
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<
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<
s
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">N Π.
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</
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<
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<
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<
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">XRH; </
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<
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XH = XR &</
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<
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<
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<
s
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xml:space
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">quum itaque ſit H Π major ſemiſſe totius N Π; </
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& </
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<
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<
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">liquet totam X Π majorem eſſe
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triplâ X N; </
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<
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xml:space
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">ſeu totam N Π majorem eſſe quadruplâ N X: </
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<
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<
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<
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">Hinc perſpicuum eſt, ſi fuerit NZ reflexi N Π quadrans,
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quòd nullus alter hujuſmodi reflexus punctum Z permeabit. </
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<
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alterius cujuſvis reflexus permeare dicatur; </
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is fuerit, NZ &</
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<
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<
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">{1/4} N Π; </
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<
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<
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<
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">{1/4} N Π (ni-
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mirum è proximè demonſtratis hæc conſequuntur) quæ repugnant
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hypotheſi.</
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</
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<
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<
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note
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ciniores ſunt, hinc indè. </
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L μ, R σ ipſam N Π punctis Y, X; </
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<
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">iſtæ quidem (rectior) in Y, hic
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(obliquior) in X; </
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<
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<
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L Π; </
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<
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">& </
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<
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<
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RY. </
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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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">2 ang. </
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<
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">H Π R. </
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<
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xml:space
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<
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= YH; </
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<
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<
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<
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multo minor eſt ang. </
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<
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<
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quadruplus anguli N Π R; </
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<
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">igitur ang. </
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<
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<
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<
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<
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tur jam, ſi fieri poteſt, punctum X ipſis Y, Z interjacere. </
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<
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angulus externus NYR interno NXR major; </
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<
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eſt. </
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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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xml:space
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">Ad alteras partes haud abſimilis erit diſcurſus; </
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<
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petitioni. </
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</
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<
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<
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<
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xml:space
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">Hinc obiter patet ad eaſdem partes incidentium reflexos ſeſe
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priùs (velut ad φ) quàm ipſum N Π decuſſare.</
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<
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<
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duobus in uno puncto reflexos non concurrere.</
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<
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<
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