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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 72r, page id 00068198:0143
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alem X, y, Z aebent fache quadhatu ex non quadintis,
X=mm X = lenm
14
4 4
y- Um X Umn y = lmmn Z = lmnn, fit 1 mn
An sic X = Im y = In Z = mn fit xyZ = ummun. Ut servetur ex homoque crectum; sit
ete qu+ha = lm
Av. + hb = In hv + he = nn
h sit unitas
seR Ca C = n: V = ln: h = b. Ergo fit In - hb + ha = lm et ln - hb + hC = m
et fit e lnn -hbn L han =(Cmn) = Un = hbl + hel, seu
sit
a
ulet 
ubi si facias quaeras n per l pervenies ad
radicem quadraticam, quae non cedet quae si lae. Ergo
LMM
c
 Ergo fiat hv + Ra = Impp ho hv+ hb = bngq
E2∞ + EC = MMYY
quem ipsius tix valorem ex media aequatione sumtum
_ AV = ln9q - kb. Ergo Inqq hb +ta substituendo in pnabus extr emisfiet:
langger - sibn rr + hangqrr = (Ima pprr) = leg9p = teblapo + ucpp
aeret Ranrr help: llnpp -hblpp lnner + bbneY
99
re pp: rr faciamus g9: hh, et fiet h an -t a h Cggl:, Uggn hl au gglln - hbgsgl- hhlun + titbbn qu
aplicemus n per L faciendo n = 1ol + rh, et ita videamus an mudponi, denominator per numeratorem
de
divisibilis reddi possit. ita enim ae res reducta esset ad desederatum: ot nec tantum 10 et 11, sed etia in g)
+
apy 1
crbutraria erunt.
15
C
Effici posset si han hC gy( ficret CfL; et seu si frecel
cgge: tea A = th st + cggl
Ergo oportat  ut faciendo BEan = hC. 99l = hS f, seu, R= hhfC + cgahhf+ cg9) : ha
das+hage
se
s
AA
ta tollendo R, tam iumerator quam nominator, divisibilis erit per L, et F evanescet l in
C
numeratore manelutque solum U, l et l in denaminatore, quae est formula aequanda
a
e
a
quadrato, quod semperr fiegi potest
=anrr = seblxp = Rburr = teclpp: Unpp = IYr
seu 99 = Krr (a - b)n  K pp (C. b)L,: Unpp lnnrr siat p: Y = foh ubi a, A, Y et ) dive 6, l, p permutantur
id est si rubique pro a, n, Y ponas respective C, l, B prodit idem
quod nate et n ge 20t +21h, etate adi tollere simnl
g4 = B (a- b ) F hi3+F1b-c) l: H nor t fIn - hhat nin Explicavi  per 10ta + 1A
Sit p. r= H. t.
et uet explicatiorum factam tentavi tollere aint go
et
eo
expcemus
0+
A sed non licuite
sit set (a b) n + f (b-C) l = hhgl adeoque numerata erit divisibilis
per l,  jam et nominatorem, hoc modo per  divisibilem esse praevidemus. Fit n = Chhg - ff 1b- c)) l, : (a - b) hh
piat. hit  b)na
intiltminatu non ibit ultra quadratam.
vel per compendium n = el: R et fiet g9 = thgl :, s C ppes
seu 99=
1
ata pp
 ppll ell. h) et BC (3t h
., PCl - heell. et g= t ut
Lf h ihg , lV (hppe- hhee)
i