# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/797435492:0294
# Permalink to this reading: https://leibnizlegible.com/page/797435492:0294?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 70, page id 797435492:0294
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=294
# Source image: https://digitale-sammlungen.gwlb.de/content/797435492/jpgs/default/00000294.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 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.

 C, T.
nc
(b(EI. Lecto
(5) Constr.
(4) 27. Leclo
Uod insressi lumus iter accurum recta proscquemur.
l. Sine rectae A B, VD sibi parallelae; quas secat posirione data
DB; tranleant vero per B linea F B F, FB F ita ad se relatae, ut
ducti quaris P C ad D B parallela, sI pervetuo P F inter P C, P F
eodem ordine desisnaro media Arithmetice, tansat aurem recta BS
Curra F BF. Oporret linex F B F tangentem (ad B) delionare.
Sint Numeri NI, M proporrionalium P F, P P (quales (a) explicu
imus supea) exponentes; tatque H. M:: DS. DI; connectatur.
que TB; haeclincam F B F concinget.
Nam uccunque ducta sit recta P C, dictaslincasfecans, uei cernis:
EAgue FC. EG (b):: H. M :: (C) DS. DT:: (d) L 6. RC;
cum ergo (c) sIERC IF C; eric L C:  2 F C; unde liquer rectam
TB extra curram F B F. roram conlistere.
IL. Reliquis perstancibus iildem, CiE jam P F inteF PC, PF media pro-
portionalis Ceometrice (eodem ordine media nempe, quo tuit prius
Arithinerice) eadem B I curram F B F continget.
Ftenim e mediis Arichmerice Geometrice que proportionalibus hoc.
ce modo constructa linex sele muruo (a) contineunc ad B, ergo cum
recta B T rangat unam, haec alteram quoque continget.
Exemplum. Sit P Finter PC, PP clexmediisterria; erit er-
80M = 7; _N = 3; adeogne DS. DT: : 3. 7.
TII. Manente porro quoad cxrera proxime praecedence hypotheli
sumproque quoris in curra L. BF puncto F; etiam ad hoc punctum
tangens recta limili pacto desienatur.
Nempe per F ducatur recta PC ad iplam DB parallela, lecans
curram L. X E. in E, TM P. X tanSAE curram F B F in E; Rratque N.
M: 3
F1 94.
(a) 22. Tecto
(4) 3. Lect. 7.
useo
1∞. 95.