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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 151, page id 175905688X:0173
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=173
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000173.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.
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# After the first blank line: the recognised lines in reading order, one per line.

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C OMME HY ARLE EN LTDRUNI.
15I
quoniam componitur ex duobus quadraris linearum AHI _c FIC.
Eodem modo quadratum lineae C B erie a a L 2 a X L X X L py.
quia xe quale est binis quadratis ex BFT _ HI C. Acque adeo sum-
Ma GUadTAEOTUI Cx AC, CB erit = a a  = X X L = y7. O UX
cum eam rationem habeat ad triangulum AB C, quod est a y
Cutpote aequale semissi ejus, quod producitur ex bali A B e per-
pendiculo CTI,) quam habet 4 d ad a: crit productum ex
aa + X X F yy in a aequale ei, quod provenit ex ay in 4 d, hoc
eAt, habebitur AquatiO InTeF 2 a3 L = a X X L a y y _ 4 a d y. Sed
quandoquidem duxe suppolix lune incognita linex x dc y, alia
adhuc superest AEquatio invenienda. Guam ut inveniamus, con-
Siderandus insuper est angulus D, cui aequalis supponitur angu-
luS ACB; qui si obtulustuerie, produco linea B C, donec ex
puncto A in ipsam cadat perpendicularis AI, omminone factum
eAtcirca aneulum D. Tum, quoniam datus est angulus D, dan-
tUE quoque recta D F X F C. AC proinde (I prO D F ponatur b,
_ prO FC6, serent ipla ricem dati anguli D, Feneque triangula
ACI_GDF similia. Fadem ratione similia erunt trianoula
FTCB_ABI. Ende crie ut C B ad AB, Sic C FI ad A I, X BTI
adBI. Ouare (i pro quadrato ex C B ∞ a a F a X L X X L py brC
vitatis causa scribatuTe e, H. C., prO C B D V aa = 2 aX L XX -L yV
Ponatur e; tatque ut e 2d 2 a, sic CHI seu y ad AL: CrIE A L
2ay
D
D 2a 4 = 2 a X
Tum subductd BC Peu e ex B LPeq 2 a a + 2 a  rC
linquitur CY 2 2 a = 2 a ∞ = ee
Tam cum CF Sic ad AT, hoc eAt,
24 a + av = ee 12 a), Peu 4 a =  a X = e e ad 2a y, (ICUED F 24
d
FC, hoc ett, badc: erit = a ac - F2 ac x - c ee, productum (ub Cx-
tremis, aequale 2 aby, ei, quod tcsub mediis. Oux altera cAt
Aquacio. Acque ad haec Facienda manuduxerunt nOs Pracepta
jam cradica, ita uc nullae partes Problematis lint omillae. Fit qui-
cunque omnia penitius inspexerie, se luo marte propolitx quae-
Ctionis Colutionem ex illis huc ulque perducere pocuisse judica-
bic. Difficultas enim toca jam a fouris ad numeros sen cermi-
nos Analyricos esteraducta, ita ue, quae lupersune, cuilibet ob-
via esse possine, etiam si de lineis, punctis, ansuli(que amplius
1O