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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
# Folio 49, page id 824573315:0069
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C AP. 120
 semicircnli.
tiam (quoniam ad sensus judicium Ac provocatio) cur masis
incredibile exittimem, acucam illam Elliptin, e obculam H7.
perbolam, in iptis contactuum punctis, ad reCtaStAMBENCCS Pa
ricer non inclinari, quamris pollea rarie divaricentur; quam
ca(dem paricer luas rectas non nih in unico puncto concingere)
Nam e hoc lentui non masis credibile videbitur; neqi camen
Clavius, credo, negaret.
Ouoniam vero de contactibus in Coni sectionibus mencio-
nem Facie Clavius; videbimus _ illic omnia nottrae lencentiee
consentanca. Instantiam delumam ex opticis; quae hac eAto.
Tradic Vicellio, lib. 5. prov. 2. Aneulos incidentiae e reftexionis,
aequales invicem esse, in speculis quibuscunque, sive planis sive concavis
sive convexis: Acq; illud eriam agnolcunt Opcici omnes. Scd Be
Edem Vicellio, lib.9. Pr. 43. ORtendic, In speculo concavo parabolico
radios omnes, qui in illud ubivis incidunt axi paralleli, ad unicum idemque
punctum, qui Pocus dici solet, reftecti: Ouod e post illum agnol-
cunc alii Opcici. Hloc aurem ut demonstret, oAendic, ex APOl
lonio, lineam incidentia,
et lincam refectionis ad
locum, angulos aequales
cum recta contingence ta-
cere. Verbi gracia. Sic
punctu objecti, O unde 2d
Socculi punctum P ducatur
recta OP, axi parallelas
inde aucem ad Focum PF:
Frunc anguli OPT, FPC
(cum recta tansente C PY Facti) aequales; uc Vicellio eX A-
vollonio demonstrat; idcoq;, inquic, retexio hiet ad punctum
s: acq; idem hec quodcunq; sic punctum speculiP, in quod
radius OP exi parallelus inciderit. Ac oporcuic octendistes
non cam angulos OPT, F PC, ad concingentem taCtOS, 2.
quales esse; quam OPB, FP A, ad speculum Factos, 2qua les
else; ansulum nempe incidencix _e refectionis in lpcculo. Vel
igicur aequalicas angulorum ad rectam concinsentem, eandem
intert aequalitatem ansulorum ad speculum; vel demonstracio
non procedic. Cum isitur demonstracio haec pro lesitima lo-
lec, quod sciam, ab omnibus haberi; dicendum est eandem 11-
crobiq: esse aequalicatem. Idcog; cum a quales sinc cam O P T.