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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 15r, page id 00068229:0029
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(1) Num L.
(3 .0. - 1
B).... HII
ac
Pres Numeros invenire
quorum summa sit quadratus, et summa Quadratorum
X - ab - a
(4) summa Numerorm. X
sit quadrato. Quadratus.
Ejus quadratum ab
.. ... a
X - 2abX + ab
= 2a + arc
Quadratus per primam conditonem. +2 abc
(5) summa Z uadrutorm, X + + X C + 6 X C + +X C + et
duas
(6) Aequatio inter summas
Quadratorum, (5) et (6
(7) Ponatur a re.
(8).. . .. + .
(9).......
(10)....
(11) Ponatur
bf +X
CH9 +X
g7- f
qui est quadrato. Quadraty ab + + X +F C, per secundam conditionem.
+X) + 4 CX +6∞X2, rab X e X + et al o
fic
d
rl 12ac.
uad
(12) dequatio  Resermata
s. = 4X +bC X + rbX + 2∞X  X ,e - 2eb  2eC - reb C pp o. dinsir milyses e.
iere
(28.) (+2X.)
fiet 2f X regX 0. t
et -+e X - 2f2
(13) Ponatur C p. m f e t ex aeq (12) fict: m f - 4 mX - 2 f +10
(19) itequatio simplex quaesita, f p) aml X
(15) Determeratio
Regressus
(15) Numer quaetit.s 2. ab
116) ......... I aC
2abc
 aX 60X) b2 fX + 292 tex re et  ( resx
M2 - 212
X amle
()m)
m- 2
n l -213 + X
ma- am l+ 412
1 - 16 m lX 2 + am: X 2- 8m l2X2
M+- Am l + 414
(17) .. . . . . . . . . . . . 11: ~ - ab - ac py M4X  - 4m L. X + 4 V+ X - 8m 2X + Bbm l X
m = 4m (2 + 4(7
sive + 4 (+ X 2 - 7m X2 + IL M T2 X 2
X p n f. 2lf
4ml
M4- 4m l + 414
fiet: ut fractio praeveniatur, et fiet:
X H m h = 2h. Atque ita valor ipsur X non
habet alium divisorem quam unita
4mehi  a mh r nih. ret  16n ti tAa t 2- 8 N Ch
E 3
= 16m el + am h= 8m P L
mhi - 4m (k + 4(7 h (∞16 m te D = am h + 8m Ih
+∞100) -.. .. +.
Sive 7 m h + 12 m l’h + 41+ F
Qui calculus cum ejusdem forme Numeros
exhibeat cum priore, potuit omitti
Restat ut inter scopulos nihilo-minorum enavigemus, sive
m ita assumamus, ut omnes nuneriquaesiti fiant affirmatior.
Caet
20n
4C
de
et
ex
0
Prubandi calculi causa,
ponc M p 1. et X  1. tunc
numerus Y. erit 12, secundi
erit -20. tertius
erit 9. Quorum
summa L, nempe
Quadratus; et summa
quadratorum 625.
quadrato quadratus
3
ab
(19) Ponatur
(20)
fn amh
 Regressus
(21) Num. quaesitus 2..
A
(16) equatio sim plexquasita
determinatio