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# Title: LBr. 560 · L'Hospital
# Folio 32r, page id DE-611-HS-855907:0063
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-855907&page=63
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# Lines: 40 recognised, mean confidence 0.86
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omnis quadratura termini quem ingreditur 
M potest recua  (posito M dari rationaliter integre ex X) reduci
ie M.
sit ergo dy = X Im fiat y = n Im. Ex 2 fit du = dusm +ndm
vel  dus = 2m an +ndin Im : 2m. Ergo ex aeg. 1. et 4, fit
2Ym
X = dn + nam. Ergo si possibilis est solutio in ordinariis, oportet
e 
n sumi talem pro n sumi tatem torulam per X,ut nam
2M
ob datam m per X, saliter n ass talem pro n assumi formulam ex X
utn nam sit integer in indeterminatis, et quidem qui sit X.
agdp- xdq + pgam
ut an + A
am
fit n =  fit dn = ag dp -pd4: 49e fint X=
ap
Xe = 2amgdp -2ampdq + apgam, : 2 m ga
oportet apgam dividi posse per m et rampaq rapdq dividi posse per q
et 2a dp - 2apdg e apam nursus dividi posse per q. quod vx
quod non facile fiet, nisi p sit div. per 4, quo casu n erit integer
 si P et con sint
m
sane videndum an rapdq dividi possit per 4, nisi
primi inter se. video id esse video id esse impossibite, in indetermi
P et q esse primos inter se ob n = at
matis: itaque jam supponunu et R
ergo sequitur n esse integrum.
itaque nam esst integer
am
  dv =ds _b_ + G, dus  dv = XV + nH) + pdy, fiet
M
9+edu = v + n y + 
dy fiet Lalb. y + bdy + dedyt cddy =
=de +ndy + any + padu + apdys. Ergo tandem fiet
db y + bdus + dedy + Cddy = b y + c dy + ndy + du y + p ddy + ap dy
et res est reducta ad unicam literam
e
drggmodt
omosgur gel sup 5, deb Lngu jum dlnplsu heo