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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 427, page id 175905688X:0449
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=449
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000449.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.73
# 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.

e
DuS, Per P
e
nunem
reducto
commun
ASIBBEM,
cujus se
e0, qu
DE RB DUCTTOHE AE QNAXLOHLH. 427
X X ∞ - Y X + 2
erGOx F ∞ y y X X = 4y x + 4 (CU = 93 ∞ + 2 yy
∞ 3 ∞ - y 3X X + 2 yy X
47 X N + 4 X
17 X - 3 ∞
+ y4 X  2 73
seu F py X
+4 ∞3 ∞ = 4y x X L 8 X (eu
F L= X X ∞
pX .L
+a yy X = 8)
L +. 3
+ +y3 X = 26
L 169 x - 8y:
F yy ∞ - 8y
+
3
= 1  Y X = 3
X
(UMMA + y 4 X - 2 73
+ 473 - 8yy ∞0.
+1oyy = 16)
+242Y = 26
+5
Deinde conlidero unum quemque terminum leparatum ae qua-
tionis hujus deductae ∞0, _ cum hic duo tancum sint termini,
habeboinde halce duas aequationes
II.
gr. + 473 + 2077. + 14 27. +5∞0, e - 293- 8y7 - 167 - 1600
(eu 93 + 47y + 6y + 8 ∞0.
Duarum quidem aequationum, si juxta praecedentem metho-
dum quaeratur maximus communis divilor, invenietur proiplo
y. = 2 ∞ O; itauE PrOPOlicAXquatio, Cu y (it ∞ -2, dirisibilis
AIC DCFNX = 2 X - 2 ∞0.
Fodem modo, proxonatur haec aequatio
X + = = a x 3 F  a a X X =  a 3 X F a 2 ∞ 0, decurque iplam dividi
C
polle per aequationem duarum dimentionum, cujus ultimuster-
minus (IE L aa. F Co aurem xquatio illa X x L yX L a a ∞ 0, adeo-
Gue Xx ∞ - p X = a 4. Flinc, Tubrosaro hoc ralore in locuI X X
obtinebitur loco Propolica aequationis alia, in qua x unius can-
cum erit dimentionis, nempe - y3 X - a a yy ∞0.
2ayy - a
t 6cy + a A66
HIhh 2
X t∞
Cujus