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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 124, page id 175905688X:0146
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=146
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 recognised, mean confidence 0.82
# 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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124
FL OR ZM ONBE DE BE A R N F
Crieque L. N ad M N, uc quadracum à P Hi ad quadratum ab NI N.
FIinc (iL NroceturC; erit c adf, licut quadratum à P EI ad qua-
dratum ab NN, hOc CsF, VE GUAdFAEUII Ex AD ∞X = L yy ad
Quadratum ex DB ∞yy Lbb = = b X F x. Ac proinde productum
extremorum erit aquale productomeciorum, hoc cAt, fx2 + fyy
∞cyy +6bb = cbx FCx 2, de per consequens, cpy - fy y ∞-
cbb F 6bX = 6∞ F fN, dc denVOyy ∞ cb2 + cbx- ex + fx
de tandemy ∞ V = cb2 + 2 cb ∞ = cX + fX2
Ad abbreriandum aurem hunc terminum = ex2 + fx; licet
consideremus, quod f -ce c = f exprimant semper unam c27-
demque differentiam, quippe qua estincerc e f, ctiam (icmajor
sic quam f(dum in opcratione lupponimus h∞c = f); Cemper
eamen habebimus =cX2 + fx7
cu
∞ == B∞2
hoc est x Simpliciter;
ad eo uc relinquatuF p ∞ N = cb2 + 2 cb = = x2. Id quod nos do-
cet, locum esse Planum, cumque Circulum existere: cum habea-
tur =x ansulusque A G D SICrectUS, EC aa m ∞PZ2; neque
enim hic habetur a, neque Z; acque mipsi p aequalis supponitur;
cum nulla ipsix Tractio adhareat. Quibus ita constituris Circu-
lum hoc modo inreniemus.
Terminus, qui centrum nobis exhibere debet, est aom
2PZ
ex
quo nobis praeter nihil inserrit: cummipsi p sic aqualis; hoc
est, proeorantum habebimus  Acidcirco, postquam linca
LM EgUatuXC- f, Sitat ut linea LM ∞c = fad lineam L. N ∞C,
ita linea AB ∞ b ad lineam AC, crit linea AC ∞
de pun-
ctum C cenerum Circuli. Sumendum autem id erie ab A ver-
sus B, quoniam habetur - 2 cb v
respondensipsox. Praeterea,
quoniam in Circulo latus rectum sc eran (versum sibi invicem sune
xqualia, alterutro tantum eric opus. Formula aurem laceris recti
hic est Vo2 2 Amp2. Vnde quidem illud, quod nobis in hoc
exemplo inserrit, non aliud erse quam V 00 - 4 m 2, hoc est,
quod,
quod,
AC+
adhuc o
ate; pe
eltabt, 1
tab
laterui hI
terbd liueal
CdeqeS
al inICem
AE, ee
lum
julque
Guandoqu
nus geadrate
iel vireu