Barrow, Isaac - Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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10284 -CEq. CEq - CGq : : CNq - NEq. NEq : : CEq. NEq.
quare permutando 4 CGq - CEq. CEq : : CEq - CGq.
NE q. (hoc eſt) : : NGq - NEq. NEq. ergò componendo
4 CGq. CEq : : NGq. NEq. & ideò 2 CG. CE : : NG.
NE. quare 2. 1 + CG. CE = NG. NE. vel 2. 1 = NG.
NE + CE. CG. hoc eſt NZ. GZ = NG. NE + CE. CG.
unde liquet, è mox antedictis, propoſitum.

XII. Ex iſta porrò conſtructione facilè colligitur, ſi fuerit 3 Rq
= Iq - Rq (hoc eſt ſi 2 R = I) adeóque CQ = CB; quòd hu-
juſmodi punctum Z non aliud erit ab ipſo D; ſeu perpendiculari ipſi
AB debitam imaginem ad punctum D conſiſtere; eas verò quæ reli-
quis refractis conveniunt ejuſmodi imagines intra circulum omnes, vel
ſupra peripheriam extare. quinetiam ſi fuerit 2 R & lt; I, adeoque
CB & lt; CQ, patet nullius refracti imaginem in peripheria exiſtere,
ſed omnes ſupra ipſam. Enim verò in his caſibus omnes refracti ax-
em AD ſupra punctum D interſecant. verùm ſi fuerit 2 R & gt; I (uti-
que ſicut reverà quoad pleraſque cunctas in hac rerum natura pelluci-
das refringentes materias uſu venit) utì reipsâ datur ejuſmodi punctum
Z, in perepheria TD alicubi ſitum, ità facilè poterit iſto modo de-
terminari.

XIII. Obſervetur porrò ſic definitum punctum Z circuli partem à
D verſus T per radios quadranti BT incidentes illuſtratam terminare.
Omnes enim ipſo MN obliquiùs incidentium refracti ipſam NZ ſupra
Z verſus G decuſſabunt; adeóque ad partes ZD circulo impingent;
item omnium ipſo MN rectiorum refracti ipſam NZ infra Z verſus K
interſecabunt; & hinc etiam in arcum ZD cadent.

XIV. Exhinc apparet (id quod _ab eximio D. Sluſio_ monitum ami-
11Fig. 127. cus mihi communicavit) potuiſſe _Carteſium_ ſine tabularum confecti-
one ſuum _Iridis_ angulum determinare. nam aſſumpto arcu DY = DZ;
angulum iſtum arcus ZY metitur; poſito circulum propoſitum per
aquei globi centrum tranſire. quod ità facilè conſtat. Radii cujuſvis
diametro BC paralleli MN refractus NZKreflectatur in ZF H;
& ZF in FO refringatur; ſitque FL ad BD parallela; ſumatur eti-
am DY = DZ; & connectantur CZ, CY; dico angulum LFO
æquari angulo ZC Y. Nam imprimìs ob ZN, ZF æqualiter ad pe-
ripheriam inclinatos, patet angulum OFHangulo PNZvel CKZ
æquari. igitur ang. HFL- HFO = ang FIC- CKZ =

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102	84
103	85
104	86
105	87
106	88
107	89
108	90
109	91
110	92
111	93
112	94
113	95
114	96
115	97
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117	99
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120	102
121	103
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128	110
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130	112

Scan	Original
101	83
102	84
103	85
104	86
105	87
106	88
107	89
108	90
109	91
110	92
111	93
112	94
113	95
114	96
115	97
116	98
117	99
118	100
119	101
120	102
121	103
122	104
123	105
124	106
125	107
126	108
127	109
128	110
129	111
130	112

Scan	Original
101	83
102	84
103	85
104	86
105	87
106	88
107	89
108	90
109	91
110	92
111	93
112	94
113	95
114	96
115	97
116	98
117	99
118	100
119	101
120	102
121	103
122	104
123	105
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125	107
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130	112