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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 347, page id 175906937X:0371
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=371
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 recognised, mean confidence 0.87
# 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.

tX
XH.
en
e
D E MO HS FR A FTOHFBRS.
Cumenim ex hypochesie AD B sit ae quale (IO ex C D,
aX = b X F X X ∞ bb. F. 2 b X - L X X
ablato utringue ∞ l0 suB C D S D B,
bX = X X
erit aD sub AC _ D B aequale ∞10 sub C D _ CBb.
aX ∞ bb. + bX.
Rursus auferatur utrinque D sub TC vel C B_ BD, id est, bx
eritque D sub AI_CBD aequale FIC Cx C B d.
aX = b∞ ∞ bb.
FToc es, relolura aequalitare in proportionem, erit
uE ATad IC vel C B, ita C B ad BD.
a - b - - b - b) X., OUod CraL prOpOTIEUI.
Duoniam autem praestare videtur, loco horum aequalium
rectanculorum considerare laterum proportionem, quandoqui-
dem in demonstrationibus Ceomerricis, ubi hae aequalitates vel
proportiones schematum contemplationi insuper sunt astrincen-
da linearum haec inter se collatio simplicior est censenda quam
planorum aui solidorum, ipsaque etiam ficuras requirit minus
intricatas, vel saltem ratiocinationes, quae circa illas fiunt, ma-
eis liberas reddit: idcirco convertenda erit aequalitas in pro-
portionem atque haec eou sque continuanda varieque transmutan-
da utendo sc. ad id modis arcumentandi libro so Flemento-
rum expositis, donec appareat quaesitum ex tribus prioribus
proportionis terminis constare seu inveniri posse. Quod ipsum
ut rectius percipiatur, visum nobis fuit aliam praecedentis Theo-
rematis demonstrationem hic afferre, qualis illa a prinsipio us-
que ad finem per propercionalia procedit, es prioribus aquali
tatibus ad amussim respondet.
Etenim cum ex liypotheli sit
OADB aequale FTO Cx CD:
a N + b X F X N ∞ bb F 2 b X = X. X:
XX 2
a Per 1 se.
cundi.
per 2 se-
cundi.
C per Y se.
cundi.
d per 3 se-
cundi.
Per 17
Sedisi.