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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 25, page id 797435492:0045
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L. B C Y. TII.
obliguiiis quam D B.) FTOruM rerO refracti sine Ba, BA; dico an. Fig 21.
sulum 6 B a majorem esse angulo HI B s. Nam ad B Pin perpendicu-
lari libere sumpram diamerrum constirmatur semicireulus BCF. cui
occurrane iplx A B, D BprotractX ad C, II; nec non ipla B a B s
punctis an s. Fiac autem angulus C BR aequalis angulo HB s, vel
arCuSCR arcui HIS, connectacur etiam recta sO, secans iplam P R
in X. ducarnur que deruo subtenla G s, FI s. Tam ob angulos PC s
PHs Pares (arcui quippe P s insistences ambos) et angulos P R,
HP s ex constructione quoque pares, erune criangula CP Z, F13. 22
HIF s inter se limilia. Ouapropter exit PC. P X:: PHI. P s. eAt
autem e lege refractionum PHI. P A:: P O. P a. QuarCP C. PZ:3
PO. P a: unde PZ = P a. esE ABTeM P X mInOT qua PR (quia
cota subtensa C s intra circulum jacet.) Ouare P’a inor est quam
PK: adeoque P R secabit angulum C P a. QuaobreM AECUS Cx a Ma-
jOr erit arcu OK, hoc est arcu HId. e idcirco major erit angulus
OB a anguloH Bs: Q. P. D.
Procedit haec demonstratio quodd casum, ubi IL= R (vel cum ra-
dius e medio rariori densius ingreditur) at exinde quoad alterum quo-
que calum facile deducitur conclusio.  Tam li vicissim a B, AB Con-
cipiantur incidentes, erunc ipsx B A, BD carum retractae; ac etiam-
num anguli ae BC, s B II erunt anguliretracti.
Hujusce Theorematis apud Periconium habetur alia demonstra. DiopI. Prop. 4.
tio. Conter Todes, _ utramris elige. N0s quam res obculit
poluimus.
VII. Inisto refractionis casu, quum Lminor cs quam R, C anguli 
incidentiae, puta anguli D B L, rectus sinus PHI, ad sinum corun se
habeat ut l’ad R; nullus incidente D B obliquior radius medium F P
retractus ingredietur, aut penetrabie.
Nam penetret (steri DotesE) obliquioris alicujus AB C retractus
18. 23.
Ba. Frit ergo P(. Pa:: (I. R::) +PHI. PB. Cst autem PC = Hy porh.
major quam P H. ergo P a major erit quam P B. quod plane
Reri nequic. Ergo AB non retringetur in medium ipsi F F sub-
jectum.
VIII. Angulus incidentix major ad angulum cuum refractum ma-
jorem habet rarionem, quam ansulus incidentix minor ad retra-
elum suum.
Fric scilicet (in figura numeri Sexri, cujus huc apparatus transte- F18. 21, 220
TACUL) anB. CBP. aBP. E ANS. HBP. SBP. Iam crianeula
 l a.