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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 43, page id 175905688X:0065
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=65
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000065.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 68 lines, status machine
# Lines: 68 recognised, mean confidence 0.78
# 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.

cc
linea,
la
a
t
cnlate
diame.
equacio
O
ay
cdy +
Oce
oa
cctd200
acta H1.
AC; sed
Pocerie
enirI.
utrod
recta
la, ex
hrabeat
lincam
C: ld
C adH
bic
2DBa dBCI a D US.
biEu in CUE
Va, supponO,
quantitatem,
qua C I supe-
TAE F A, esC
ad illam, qua
C A (UPeFaE
GC, licut d ad e: ita ut si prior illa quanticas indeter-
MINaEA VOCCtUT Z, F C SE C L Z, G C vero b-
Deinde ponendo MI A ∞ y, G7M eric b = y, _ FM
c- Fy: _ quandoquidem criangulum C MI Crrectanou
lum est, si auteram quadeacum ex C MI a guadrato ex
C C, relinquetur quadracum ex C MI.
ec 77
a d
2be9
a
2by - y7. Non secus, A a guadrato ex F C auteram
quadratu ex FM, relinquetur itidem quadtatum ex
CM in aliis cerminis, videlicet
6Z.Cy - 19.
Vnde cum hicermini praecedentibus sint aequales, osten-
dUInEy SCU MI A FOTO +d 22 + 2cdd 2 = e ez2 + 2 b d e2
2bd d F 2c d d.
AC
proinde, substituendo hanc summam locor in quadeato
ex C M, invenietur, illud exprimendum essehilce termi-
15 bd d22 = cecze = 2 bcd d2 - 2 bcd e 2 - y Y
bd d + cdd
Porro suppono, lineam rectam PC OCCUEFeTC CUEVX
C E ad angulos rectos in puncto C, Faciendoque P C
25, _ P A ∞ 2, ut ante, PM crit v = y; habebiturque
propter triangulum rectanoulum PCM, 55- ∞V +
2V9 = y y pro quadrato ex C MI. Vbi Si rurIUS PTOy
substicuamus summam ipli aqualem, exurget
yy = b0d d2 - 2 bc d eZ - 2 cd d∞2 = 2 b d ev 2 - b d d55. + b d d V V
bdd L cec. + eer = dd~
cdass. F cdd 0~ ∞ O, proxquatione, quam quaerebaus.
Postquam igitur invenimus ealem aequationem, non
a ucemur ad cognolcendas Guantitates X, y, rel Z, qua
Hic