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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 125v, page id 00068200:0252
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5 1431+ 14 aequandqus quadrato, fiat quadratum a latere S_- l rl.
ans qu set equatio: (5). (145 1F1, ( 25 1+ 25 r1 ( 19- 2B r +, 2 a
Hiec aequatio  Reformata: 12 l 5 p 2r l5. 2lr =  10
fiats Unde erit 5 Cr - 2Vr. diide
tone sp Y P fiet rpV Ir - 212 1217- 2r
121 ir sive
x2 lr 2P
F
12l - 2Y
o Intelligatur p e n +2nt + 12 et Yr 4+ H, fiet:
Ponatur tnt a ul ( tG
fiet hp
si r ur, est quadratus
n + 2nt
et altera aequant erit. quargul 14
2b quqimtntntqureha
=2k
+12 l n 4 + 2nlq + l9 4
----
multiplicetur per 12C= 2rl, ∞. F hn + ahul +ht C29
erit adhuc quadratus, id est + n + 2ut + 12, 2qV
r= 2 lY, multiplicetur per
I2l- 2rl, fiet:
12tr - 24Br- 27 l + 417
sive 16lr - 24Br - Erl
Multis aequetur quadrato
a alr + fl
fiet (Il 17
1(16 (r) - 24 137- 21
ponamus ar + + f2l fit
fC
12- 2r5 2Br +Y
pone rasf Irt -2 1t fir WM
snrato q
2 = 12 + 152
na lp 
fit siqua
tn artiul + h1 C +2
v  B q+h - 212
R + 2nl +F, ∞- 12lh +1h
+lk - 2 1
Quaerenda jam esset talis explicatio ipsii
h. vel n. vel g. vel duorum vel
omnium ut numerus cognitus 214 vel
ab uno vel ab utroque latere, si distributus utrinque est, ev anescere
Certaque ars ac methodus ei rei, quippe omnium utilissimae praescribi deberet
12l+ 2qth.
v 4u+ 29h +k 2
121 94h
28
4 25
46 46 240
4s 96
1200
Cqtt 
Ergo V multiplicatm er ii ()h B Aet - a P videamu an h = H hl + 1e1 L
H (121 21 sio) (121 -8
sit quadratus at 113. non est quadratus, hoc ergo non succedit
8lar+ rX+24 Tota ars solvendi problema ejusmodi difficilia in eo consictu
methodus aliqua sit repetitis quantum opus est explicationibus f
venore si possibile est ad destructionem, coplicando itrum h, habebinus verbi H
gralia
(07. 29, 411)  8l- 29 g+1(5) confruntur 2st 7 d acd  co
74
possit, quo facto di deprimi poterunt dimensiones utrobique:
BIrs + f l +24Brt2VloB B+ V fet 2t
pone ve fBur. fiet.
Se Y +fr +f
Ergo l4
h + idh
n + ul + ( ∞ 42h, p, C  qh - 213
Sper Epohe vel sic n rul +
2r( + e, rH e
8l sa 
2al
(I 13 12L. 29. 2h
reductis omnibus ablata fractione
rI. Atr d 2t.
5r= = si 
n.
iI-2r
qp. Flp p 19
 l rt qu+2gul + q+ hn + rhul+h, lg+th. S
5+ co p - 2V cor
1212- erl
12l=2rl
A 5
t..
81-29
g
At fp. Y. fier
ergo HEHgE I 2b
sie r-nr+ i
gth huc siperar
4ry q+2, fier