# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/797435492:0100
# Permalink to this reading: https://leibnizlegible.com/page/797435492:0100?run=74
# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 60, page id 797435492:0100
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=100
# Source image: https://digitale-sammlungen.gwlb.de/content/797435492/jpgs/default/00000100.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.88
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

F18. 83.
L E C F. VITI.
bilecaE anoulum ANK. eriE AXT. PYR:: AT. TR. =+AB:
BK. Quare ti L. AB F AN. NK 1BZ. AB + AB. B. R
communem adsciscendo rationem B Z ad A B). est autem BL.
AB = AN, NR = CZ. AC + AC. CK =CZ. CK et
BZ. AB -  AB. BR = BZ. BR. ergOCZ. CF 2BZ. BR.
permutandoque CZ. BZ: 2 CR. B R. quin ee componendo C B.
BZ= DCB. BR. ideo que BZ C BR; quare punctum Z centro
propinguius est, quam ipsum R: 1. F. D.
Coroil. Ilinc li puncta Z, C fuerint limites punctorum radiantium
A, a (quorum A tir à speculo remoriiis, quam a) erit CZ = - CC.
Nam elt BC. AB IBC, aB. adeoque compolite AC. AB -
aC. aB. hoc est C2. bZ - 1CC. BC. Quare componendo
BC. BZ. = DBC. BC. e inde BZ E BC.
IX. Porro, consectatur e praemissis, quod si duorum guorumvis
incidentium AN, AR retlexi GH, HR axem intersecene punctis
H, L; eriE C.L, CR:: A C 9 - ANg. AC9- AR9. I Nam
guoniam est AC. CK:: AL9- iAN9. C B9. itenque CL.
AC:: CB9. AC9 = A R9. Crit ex aquo perturBATE C. L.
CR:: AC9 - ANg. AC g AR9.
X. Simili plane discursu, AI Fverit AC. AB :: C Z. Z B.
erit CZ. C K:: AC g. - AN9. AC9 - AB9. d C L. C2:
AC 9 - A Rg. A. C9 - AB9.
ZI. Hinc perspicuum est obliquioris retlexi concurtum a CentrO
masiselongari quam rectioris; quod nempe hECLL CK. Cum
enim sIE A C g = AN qL AC9 - ARG; exit CL C CR.
XII. Tlinc necessario duo quiliber ad ealdem axis parres incidentium
restexi (quales NVR, R L) sese prius quam axem intersecabunt, pura
2d L. quo Potito.
XIII. Adnotari porest angulum C X HI vel R ZL (a reftexris oc-
currentibus inclusum) aequari angulo NCR una cum difterentia angu
lorum incidentix; vel, duplo angulo NCR una cum ans. PI AR. (Prenim
ang. RXL = aHG. ALR - ARN = ang. ACR. 1 CRI.-: a18.
ACN .) C N R = aNG. ACR - ACH -+: aNg. C RL-
CH R = ang NCR +: ang CRS -CNP. II Ouincriam ang
ERS = CNP. = ange RC A F C AR =: aS. NC A +
AY