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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 157, page id 175905688X:0179
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=179
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000179.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
# Lines: 66 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.
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# After the first blank line: the recognised lines in reading order, one per line.

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inde, cuI
ediis, et
Alocum Z
2 A A. F 11
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hoc ell.
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aperestu
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COMMENTARLL LA LIBRUM I.
157
ducto Problemate aliquo, in quo ad iplum construendum Eres
uxponendae Cuncincoenita lineae x, Y, e Z, ad duas Aquationes
∞ X ∞ - F =CX -  bb, E yy ∞ a A -F 2 ZX - X X, PrOinCOGMIEa LIBCdZ.
6
cuinulla respondet Equatio, ad arbierium sumi porest linca co
onita d: pocero in locum duarum praecedencium AEquationum
leribere _ N ∞ L6N = bb, d yy ∞ a a F d x = x N. Elinc cum
L d = 66
26a
duxe supertine linex inveniendae X _ y, ordine quoque utenda
erir unaquaque sEquationum reliquarum x x ∞ F = CX L bb, e
Ld = cc
Yy∞aa F AX = XX sire eaS ConSiderandO SEpATAEII CIVC UnAI
cum altera comparando, ad explicandam unamquamque ex in-
coonitis lineis. Onocirca considerando separatim Aguationem
Yy ∞aa. F dx = xx, cum, quancitatibus- 1 a a et -- x x ad altc-
ram partem sub contrario signo tranctaris, tat 2 d X ∞y y- L X X
=aq: hinc si in altera Aquatione x X ∞ F CX F bb prO Z d X
Ld  c
Substimuatur yy. L L X - a a, habebo Aquationem X. X B = CV
= yy. = ∞ N - a 4, - + bb - 66 - yy = 26a. FIOC eAt, demptis 2-
qualibus, ordinata que aequalicate, habebitur 2 c ∞ ∞ a a- L. C6
= bb. F cd. FC FC, dirisa utraque aequaliTaTIS PaPtC PeF 263
X 3 aa. + cc - bb + cq
x excognitisa, b,c, ex ex ad orbitrium sumenda d sic invenienda.
Tnrenta autem lincax, ut habeatur v, oporret tantum in A. qua-
tione luperiori py ~ a a L d x = x x in locum x Cubrogare ralo-
et in locum x x hujus ralorem.
e Tegy ∞ : a abb +, aacc + - bbc0 - a + -b+ - c4 + + ccd d 211-
c, Ca