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

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7961 CAN = ang. NCR + NAR. itaque rurſus ang. KXL =
2 ang. NCR + ang. NAR. liquent igitur quæ propoſita ſunt;
in uſum (ſi fortè) ſequentium. pro quibus itidem hæc proponenda
ſunt.

XIV. Etiam palàm eſt è dictis ipſos reflexos GN, HR directè
11Fig. 83. procurrentes à ſe divergere; adeóque duntaxat unum hujuſmodi re-
flexum oculi centrum tranſire; conſequentèr & puncti A tantùm u-
nam à convexo ſpeculo imaginem exhiberi.

XV. _Lemmatia_ 1. Sint quæcunque tria quanta A, P, C; primó-
que ſit A. B & gt; B. C; dico fore A + C & gt; 2 B. ponatur enim
fore A. B : : B. E. erit ergò A + E & gt; 2 B. quinetiam erit ergò
B. E & gt; B. C adeóque C & gt; E. ergo magis A + C & gt; 2 B.

2. Sit (iiſdem adhibitis quantis) ſecundò A + C & lt; 2 B. dico
fore A. B & lt; B. C. nam ſive dicatur eſſe A. B : : B. C. vel A. B
& gt; B. C. ſequetur utrobique fore A + C & gt; 2 B; contra hypothe-
ſin. itaque potiùs eſt A. B & lt; B. C.

XVI. Etiam hoc adjungo. Si duo ſumantur ad eaſdem axi partes
22Fig. 84. (circulíque convexâ parte comprehenſi) ſibimet æquales arcus NR,
R X; & ducantur rectæ AN, AR, AX; erit ANq + AXq
& gt; 2 ARq.

Nam ducantur CN, CR, CX; & demittantur ad AC perpen-
diculares NE, RF, X G; ſint item NP, RQ ad AC parallelæ
ducantúrque ſubtenſæ NR, RX. ; & quoniam ang. RXQ & gt;
ang. NRP; patet eſſe R X. RQ & lt; NR. NP; adeóque cum
RX = NR, erit RQ & gt; NP; hoc eſt FG & gt; EF. ergò 2 CF
& gt; CE + CG; unde 4 AC x CF & gt; 2 AC x CE + 2 AC x
CG atqui eſt ANq = ACq + CNq - 2 AC x CE. & AXq
= ACq + CNq - 2 AC x CG. & 2 ARq = 2 ACq +
2 CNq - 4 AC x CF. ergo ANq + AXq & gt; 2 ARq.

Addo, ſequentium gratià, ſi punctum A ſumatur ad alteras (inſra
centrum) partes; & reliqua ſimiliter apparentur; fore contrà, tum
ANq + AXq & lt; 2 ARq. nam in eo caſu eſt ANq + AXq
= 2 ACq + 2 CNq + 2 AC x CE + 2 AC x CG. &
2 ARq = 2 ACq + 2 CNq + 4 AC x CF. unde liquet pro-
poſitum.

XVII. Sint jam ad eaſdem axis partes duo quilibet æquales

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