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

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6749 metam infra quam nullus reflexus axem ſecat (vel perpendicularis
iqſius reflexum BZ ad Z terminari). quia ſemper Cv & gt; CZ;
adeóque CK & gt; CZ.

VIII. 2. Patet eſſe KN = KC.
3. Patet fore PN (2 CQ), CN, CK {. ./. .}

IX. 4. Ductâ tangente BT, productâque CNE, patet ſecan-
tem CE diftantiæ CK duplam eſſe; & EN = 2 KZ.

X. 5. Manifeſtum eſt incidentis ad F (hoc eſt ad diſtantiam 60
11Fig. 64. graduum à vertice) reflexum per verticem B tranſire; proindéque
reflexos omnium intra BF incidentium axem intra ſpacium BZ decuſſa-
re; ſed omnes _extra_ BF reflexos ultra B cum eo convenire.

XI. 6. Perſpicuum eſt duorum hujuſmodi quorumvis ad eaſdem
22Fig. 65. axis partes incidentium (ut ipſorum MNP, QRS) reflexos (ut
GNK, HRL,) productos ſe prius decuſſare, quàm axem. Nam,
ductis CR, CN, eſt C ρ & gt; Cv, adeóque CL & gt; CK. unde ne-
ceſſariò rectæ NK, RL, ſe decuſſabunt, puta ad X.

XII. Hinc ipſi convexis partibus incidentium reflexi, NG, RH,
antrorſum procurrentes divergunt; adeóque nunquam uno plures
idem oculi centrum permeant. unde ſpeculum convexum unicam lon-
ginqui radiantis imaginem reddit.

XIII. 7. Notetur autem angulum GXR (vel KXL ) à duobus
reflexis comprehenſum æquare duplum angulum NCR (hoc eſt
duplum exceſſum angulorum incidentiæ) . Nam ang. KXL = ang.
ALR - ang. AKN = 2 ang. ACR - 2 ang. ACN = 2 ang.
NCR.

XIV. Pro Sequentibus hujuſmodi _Lemma_ proponemus: In trian-
gulo quopiam ABC recta AD biſecet angulum BAC; dico fore
33Fig. 66. AB + AC & gt; 2 A D.

In _Iſoſcele_ res clara eſt; in alio proinde ſit AC & gt; AB; centró-
que A per B ducatur circulus BXY ſecans ipſam. AD in X, & AC
in Y. Subtenſa BX ducatur, ipſamque AC ſecet in V; fiátque
VT ad AD parallela. denuo ſubtenſa XY connectatur. Et quoni-
am ang. XVC major eſt angulo XYV, vel angulo BXD, vel

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