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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 177, page id 175905688X:0199
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=199
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.81
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

AB, I
illelogras
n Apollo
AE
cacibus in
a ti
l. C
II
en
a
et
te
On
eun
1a
COM M L R. T AREE IA LABRUM TI.
17n7
tem in curra sIE C. Ec in
AB quidem puncto A exi
Sente dato, ec in iplam à
puncto C demissa perpen-
diculari C B, ad reteren-
dum punctum C 2d ali-
quod punctum iplius AB:
voco AB, X; EBC, p.
Deinde, quoniam, propter
politione datas AB, DF,
datum est punctum inter-
sectionis D, data quoque
erit recta D A, HCC nOn
AF, quae ipsi AB est perpendicularis, Secans D FI in F. Denigue,
demissa ex puncto C super D EI perpendiculari C 6, producatur
CB, donec occurrat rectx D F in puncto II. Quibus politis, ut
inveniantur rectae DC, C C, ostendentes relationem, quam ha - potig quaerenda EG. (9
bec punctum C ad punctum C; POnatUFD A ∞ a, A F ∞ b. Flinc,
cum AB siIF ∞X, erit D B ∞ a- L x. Jam vero quia propier simi-
licudinem triangulorum D A F, DBFI, D A est ad A F, hoc CAt,
a adb, licut D B, hoc eAt a = X, ad BII, erit B FI ∞ ab + b ~. Cui
si addatur C B ∞ y, het tota C IIDy L b. F-. Porro quoniam
rectanoulum esttriangulum D AF, erit quadratUm Cx DF X-
quale quadratis ex D A et AF; ideoque D I ∞ V a a F b b. IIinc
Cum D A siE ad D F, hoc est, a ad V a a L bb, SicuFD B, hoc CAt,
a = X, dd DHI; eric ipla ∞ a +
V aa = bb. Similiter, ob similicudinem triangulorum F AD,
FIOC, cum SEuED F ad F A, hoc CA, V a a = bb, 2d b, ica C LI,
hoc ett,7. Fb. + = ad HIC; eric HIC ∞ abr + abb + bb x
aV aa + bB. Jux
Si Suberatatur ex D H D V a a F bb . F = V a a F bb, relinque-
tHE DC X
+ a a X - aBy
aV a 4 L bb
AA + a X - by
Y aa tbB
Denique quoniam
DF es ad D A, hoc est, V a a F bb ad a, sIcuE C FI, hoc es,
V
DB, (4)a 1H 1