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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 155, page id 175905688X:0177
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=177
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000177.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
# Lines: 54 recognised, mean confidence 0.79
# 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.

umqs
s Corinit
N est, 
rbitiiu
esponde
ed Det
CAHS
d qu0
acallela
Qualis.
uod quat
olitis rell
3, AC
eDVid
atae d ellet
ad deter
D quat
alquen
nItam.
caC A
Xd
ecetm
DeMIId
Iu
n OmMe
decet
a c
1
COMMEMYAREE EN LEBRUM I.
155
direrlos tribuerimus ralores. Ubinocandum, quod, postquam
allumpex tuerine recta A F, A F ipsi datae a xequales, ac junsatur
E F, puncta hac omnia in rectam cadane lineam P. P, adeoque
punctum quorlibet in ca prolibitu sumprum quae sico Patistacere:
cum, propcer sinilia triangula AF F, _ CD F, reCtZCD, C Fi
puncto Dubicunque in L. F assumpto) haud aliter aEque AF,
A F lemper line aequales, ac proinde BD, D C simul exdem
quae A C, C FSimul, hoc est, eadem quae A F vel q
Flaud dissimilis exie quaeltio, si punctum D inreniendum sIE, ita
ut iplarum DC, D B differentia lic datae recta a aequalis.
IT P R O B L E MI A.
N circulo ABC F crecta sup er diametrum BF pCF
Lpendiculari CD, circumterentiam hinc inde sccan-
ec in C e A, _ a B ad cam ductis BC, BD, quarum
haec circumterentiam secet in F, dantur BF ∞ a, ∞
BC ∞b: Oporteat que invenire LD DX.
hincpro BCponOy, _ pro BF pono Z: eritque O F ∞ Z
Deinde ut perreniatur ad Aquationem, considero lineairi  L
Duoniam ad quae stiBACII NALIC LOLHHCIAE, LPPOLCHC CaLE.
rectanzulum. Cndcnec  Guaalnte b) alterae
Quadrato ex BC ∞bb, reliquum bb - py lic aquale quadrato
C
ut jam factam, necessariae videntur linex B G ac diameter B F3
ip(i BF esse perpendicularem, hoc est, triansulum BC C esse