# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/797435492:0111
# Permalink to this reading: https://leibnizlegible.com/page/797435492:0111?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 67, page id 797435492:0111
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=111
# Source image: https://digitale-sammlungen.gwlb.de/content/797435492/jpgs/default/00000111.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.86
# 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.

l B C 20 IZ.
IX Adnotabimus tantum quod ex Prohlematis hujusce riatura cor.
structione que proxolira laris accendenci constabie (urique licur in HI
pochesibus antehac tractatis uberius est. declaratum) duorum tantum
ad ealdem axis partes incidentium reAexos ad unum sele punctum de-
cultare. nam aliorum unius (qui subinde. Porest dari) vel alterius re.
Rexi per ejusmoci punctum transcuntes ad alteris parribus incidenres
perrinebunt. (I Exhis quadantenus eluceseir daris puncti radiancis,
oculique politione designari porest linea quaeris, in qua dicti puncti
species apparebit; incumbic proxime punctum in ea pracilum deter-
minare, ad quo eadem contictic. eo spectat hoc Theoremation.
Z. Ab eodem quocunque puncto A manantes duo radii A N, AR Fi8. 95, 96i
in circuli reflectentis periptieria prarer illum arcum N R Cguiinci-
demia punctis interiacen) incercipinne arcum FS; corum verore-
Rexi incercipiane arcuta e 5; erit arcus es aequalis summae vel diste-
rencix dupli arcus N R, _ arcusPS. Nam (1) inprimatigura;
cA PS + SR  + RN = FN = N ∞ = ∞0 + 5R - RN. er
20, pares hinc inde SR, ec sR subducendo, erit PS + RN-
0 = RNI. proindéque PS t 2RN = ∞5. (2). in altera Egura:
exic PS F SR - RN = P N = N ∞ = RN -+ R5 - 5∞. qua
re rursus xequales anterendo SR, R o manebir PS  R N === LL 1
se unde iransponendo erito  = 2 R ( -- P 5.
XI. Erium hoc Cemmation adscribemus: Bilecetur recta AP in _, Bi8. 94.
ec ubiris surmatur punctum A; exic P A = = fL L: td A.
FA =
J+: 2A 1
P A L: AN.
lano  eI
iai
XII. Extiinc, ut propolirum cicius actingamus, Suppasico rattios HiB. 95, 90
AN, AR (quoad calum pralentem) libi quam proximosincidere.
punctum delignabimus ad quod iplorum reflexi N ∞, Rs conCurrunE:
dicimmus nrique si dicti reRexi concurrant ad Z; bilectis subten(I5N P.
NVD In F, _EF; FOrC FZ. ZH:: F A. NA. I Nam quoniam
orcus NR, PS ex hypocheli sune indefinite parri (seu minimi) se ha-
Debune uc sua subcenlx; nec non idem de arcubus e R, os dici porek.
igiene arc. PS. RH:: PS. RN 3: P A. RA. (hoc eAt ob R A,
N A nihil, ex eadem hyporheli, differentes):: P A. NA. ergo,
biscomponendo, eric PS F 2RH. RBI:: P A F ZN A. W A.
HOC