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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 84, page id 797435492:0136
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Y E C X. ZII.
CEg. CFg C6g:: C N9 NEg. NEg:: C Fg. NFg.
quare permutando 4C6g -- C Fg. C Eq:: CF9 -- C 69.
AF.4. (hoc est):: NCg. NEg. NEg. ergo componendo
+C Cg. C Fg:: NOg. NFg. _ ideo 2C6. CF:: NC.
HIF. quare 25F - C 6. C F = NG. NF. vel 2. I =N∞.
NF - CF. C O. hoc CANZ. CZ =NO. NF + CF, CC:
undeliquet, e mox antedictis, propositum.
XII. Ex ilta porro constructione Facile colligitur, (i fuerit 3 R9
I9 - R 9 (hoc Cst(I 2 R = I) adeoque C ( =C B; quod hu-
jutmodi punctum Z non aliud erir ab ipso D; seu perpendiculari ipsi
AB debitam imaginem ad punctum Dconsiltere; eas vero quae reli-
quis retractis conveniunt ejusmodi imagines intra circulum oimnes, vel
supra peripheriam extare. quineciam (i Fuerie 2R = 7I, adeoque
CB =CQ, Patet nullius refracti imaginem in peripheria existere,
sed omnes supra iplam. Fnim vero in his calibus omnes retracti ax-
em AD supra punctum D intersecant. rerum I Fuerit 2R C. I. (uti-
que licut rerera quoad plerasque cunctas in hac rerum natura pelluci-
das retringentes materias ulu venit) uri reipsa datur ejusmodi punctum
Z, in perepheria TD alicubi sirum, ita facile porerir isto modo de-
terminaei.
XIII. Obserretur porro sic detinitum punctum Z circuli partem à
Drerlus T per radios quadranti B P incidentes illustratam terminare.
Omnes enim ipsoM N obliguius incidentium refracti ipsam NZ supra
Z vertus C decustabune; adeoque ad partes Z. D circulo impingent:
item omnium ipsoM N rectiorum retracti iplam NIZ intra L vertuSK
intersecabum; ex hinc eriam in areum Z. I cadent.
XIV. Exhinc apparet (id quod ab eximio D. Slusio moniturm ami-
cus mihi communicarit) poruisse Carressum sine tabularum contecti
one luum Tridis angulum determinare. nam a NUMPEO arCU D T =-DZ 3
angulum iltum arcus L P meritur; polito circulum propolicum per
aqnei slobi centrum trantire. quod ita facile constat. Radii cujulris
diamerro B C paralleli M N retractus NZ P refectatur in Z F HI 3
_ Z F in FO retvingatur; sirque F L. ad B D parallela; sumatur eti-
am DZ = DZ; SE COnNeCtANtUE CZ, CY5 dico angulum L FO
aequari anguloZ C. Y. Nam imprimis obZ N, Z F xqualiter ad pe-
ripheriam inclinatos, patet angulum O F H angulo PNZ vet C RL
aquari. isicur ans. HIF L. = HFO = 2ne F 1C  CKL = due
ed i
Fiβ. 127.