# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/797435492:0306
# Permalink to this reading: https://leibnizlegible.com/page/797435492:0306?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 82, page id 797435492:0306
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=306
# Source image: https://digitale-sammlungen.gwlb.de/content/797435492/jpgs/default/00000306.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.83
# 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.

Ei8. 227.
l B C F. Z.
abjicienda) = 2rrm a = - 4 40 - 2gq m a = 2g m mo. Vel
rrma - 4qm a = 2 gc - gmme; vel denuo substicuendo m
Proa, et proc, AAtrrmm -49mm = 2gt qm nt; vel
rrmm-G4m m
29 qmm
=FT.
Exemp. II.
Sit recta F A (posirione ac magnitudine dara) _ CvrVa F MIO
proprietare talis, ut ab ea utcunque duet a rectâ M P ad F A perpen-
diculari Summa C AbOrUM CX AP, _C M P aequetur C ubo rectae AF.
NOMIneNEE A F = r, AP =f; unde AO - f. ). c; X AO
cub. = f - - 3ff0 -   3f0 c.) e; (seu abjectis superAnis, ex prae-
scripto) = f3. j- 3ffc. Irem N Ocub. = cub. M - a = m-
3 m m a.  3m a a - a (hoc est) = m- 3m m a. Quaproprer
est f3. 1. 3f fe F m L 3 mma = (A cub. + N C cub. =
A ECuB. =) r abjectisque datis, est 3 ffe = = 3 m m a = 0.
Peu, ffe = mma; lubrosatisque loco a, ec c ipsism, et, exit
Fft =m; seut = fC; eAt ergo P T quarta proportionalis in ratio-
ne A P ad P M continuata.
Similicer, Si fuerit AP 9g. J. MP 49 = AFgq; reperietur
EOrCPT = 73; vel PM quarea proportionalis in rarionc AP ad
PM; ac ita porro; quod de Cgeloformibus iltis lineis an obserratu:
dionum Cit nelcio.
Dig. 218.
L. C alande
Exemp. ITI.
ositione data sir recta A2, et A X magnicudine; sIC exiam curVa
 MOralis, ue ducta utcunque recta M P ad A Z. norrali, SIE AP
cMb.   P M Cnb. = A X X AP XP M.
DiCanEUE A X = b; _ AP = f; ergo AG = f  e; BC AO
6ub. =
 3
; OH cub. = m - 3 m m a. CC A OX
DI = - Fm - Fa - m e -)  aC = f m = fa = m C;, unde A X X
A ZX
=bfm -- bf a - bm e; hinc aequacio f - 3ff0
L m = 3mm a = bf m - b5 a -bme; teu aioliendo rese
ctariea