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

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

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8769

Lect. X.

1. IN poſtrema Lectione quod ſpectavimus punctum circuli convexo
alluxit; nunc parte@ concavas irradians aliud, at magìs @ π’ π ω,
contemplabimur. & quidem caſuum præcipuorum diverſitatem im-
primìs diſtinguemus. Nempe radiet punctum A in circulum re-
flectentem, cujus centrum C; connexaque recta AC protendatur in-
definitè; quo poſito.

II. 1. Incidat radius AN; & ſit AN = AC; erit ipſius AN
reflexus, puta N _a_, ad AC parallelus.

11Fig. 97.

Hoc è ſuprà generatim oſtenſis conſtat; & facilè jam patet, con-
nexâ CA. etenim eſt ang. ACN = AN C; ob AC, AN, ex
Hypotheſi pares; & ang. ANC = _a_ NC, propter reflectionem;
adeóque ang. ACN = _a_ NC; unde ſunt AC, N _a_ ſibi paralle-
læ.

III. 2. Incidat radius AM major ipsâ AC; ejus reflexus (puta
22Fig. 98. M _a_) cum axe directè procedens conveniet ultra centrum, reſpectu
puncti A; (hoc eſt centrum C puncto radianti, concurſuique inter-
jacebit).

Nam ob AM & gt; AC, erit ang. ACM& gt; AMC = CM _a_.
ergo ang. BCM+ CM _a_ & lt; ang. BCM+ ACM = 2 rect.
quare M _a_, CB convenient infra CM ad partes _a_ B; velut
ad K.

IV. 3. Incidat radius AR; & ſit AR minor ipsâ AC; ejus
33Fig. 99. reflexus, puta R _a_, axi retrò protractus occurret. (hoceſt ut radians
centro, concurſuíque ſit interjectum).

Nam hîc ob AR & lt; AC; erit ang. ACR& lt; ang ARC = ang.
_a_ RC. quapropter ang. DCR+ _a_ RC & gt; 2 rect. unde patet ipſas
D C, _a_ R portractas infra CR concurrere.

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