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.
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.reflexus, puta N _a_, ad AC parallelus.
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.
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).
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.
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).
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.
_a_ RC. quapropter ang. DCR+ _a_ RC & gt; 2 rect. unde patet ipſas
D C, _a_ R portractas infra CR concurrere.