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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 4
# Folio 1v, page id 00068001:0002
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siet ex (x 4lv P 61V. (
24) intelligatur siteq r.
t7V+ fV + f9
olv- 29. 4 alq f argH pp Aula
(21) Aeq. Reforn. 1g2..
(26) Aequatio simplex H = lq. 2 j at + + 2l9 - 29 - 12
Quasita: V H
Daterminatio ad
evitandos Nihilo-minores
(27) Num L, ab 1 e
ut vlgertaq
 21 4 10l + 49
1 + + Cv + F eq +CD 1 0
L Hoc obtentum
2o)tmll. ac H + f ev + fCq + e2B H 0
intra num (32)
 tm I1 X atac ) ev - et - relB p0 ind. X (3364)
1) Ponatur
 11 ++N
erit qp
poreq erit fictque ab  e l + Cq
Bnatur G HD erit ab pro. per () sumt ,
. Fiat P p 2. erit X abac p 0 per ()
etit X ab ac por per (2y)
si qua sia prp et X ab ac p
(2) si 20p4 fiet ac pe per (1)
 Har sol, erita + atque 29 - 1 pi Q, sive
multiplicundo per +
C150-  
2t4 (10 21p aetq (49)
solvetur, perinde ac si ita sconceptum esset:
Tres invenire quadatos, quorum summa
quadnatus IHa i summa sit quadrabus
et summa quadra quadratorum sit
quadratus, et summa quadrato-quadra-
ab 
ac H = 5 - 1-
 - ab - ac p  - 1 +3
debebat esse X - ab- ac p, tZ
ponamus 413. eri 1.
fier YH 16 - 18 -1.
Ut ergo tres numeri quaesiti frant affirmatio
ponantur aepuri quadratis, et problema
ab (I. 1 f ) + 3( (1)
ac ⊓ 26 - 3  76 -12
X - ab - ac p 169 f1 - 26
sive in integrs tres pumeri erunt: 
64. 56)
1 - 12+3+13
A13 -3 + 13 HI
169 - a (+ 10 3)- 12, ((1) (1
APne ert 1. 1++ 14n. FB - 41
(1), noque B e + + + + lq N C)() y+ BL
(3) Ego- bil 4 atev +4 biq. 7751 β. sve epatetovos
fiet:-rh el 4 2hB in rk+ hiC arh b
ive appellando l+ 2V  X, fiet rh hh n +rhianti
et HI. aequetur Ato
fiet: hen-htr
Multiplicando omnes per i6 ut in integnis
qui satis faciumd proposito. Nam eorum summa b25
quadratus c imd quadratoqua
summa quatrapn
(Y) 167281. à  409
23104 X
194481. et Geadratos
Qucuratus a latere. 21.
seu 25 - 4 seu 25 - 1 re ad fractio
nes restucta, posita 2 6. et e p 1. porst
teen- h 5 he 45ted sd H FAd  AS p, Ax +) eAB + B2
ergo prollemasie
solvi ires divanre
ueros tat
Unde A H ha n -her (2+) 8ABF- 4 ( +2EC +C H X. ergd ess 2 , seu  vergo EB ib
Bpahre + ten +hEY (+4) 8AD1 + 495 sive βpa XvdoVcos (B el (2 +) ∞AD1270 409. tmmma 625
explica tam V. exprimente, inseratur,
Nam si suo quadrati in se ducantur, actus est quadratu uactato, quad culocua
Qui valor in aequatione numeri (31)= valorem ipsius B. sed posss et XH 
et summa quadratorum ab ipss
sumna quadratorum
feris hts h Aex 1 A h+, k 2h AB t Ahs(quadrato quadratus datus. S velics quatrat quara factum ex nuntio
_Tie ducend B in Y(+) ys a β
quad itum a 25. +4
est 194481 . Quod erat
Faciendum. Et quoniam semper potest, obtineri qbatia o quado
Cunque supponatur. 4. limitibus tantum (pro evitandis negrativis) observatis sua
poste; in pelities adtine vis mrereis quamu sinne quones tel famma su duum quarato qua
erutus datus.
4096 a
ot (41) Factim ex
X. ab. ac H 62G - 16-20, 409
habeantur, dabuntur numeri tres
 (39) Factum ex
=2 410 - 12F) 4
acp50 3 e 1
et   hr ahar+ Xs
E-. (10)
1 104 a dpetu s ettu b6
fiet V, - 6 - 18 - 1
64. 6 152.
ter - Vil ponans Y Aot fiet (3, hrl- Ah
et B  Eer tvl V (+) yC
Ducantur in se terminus primus et secundus
Sadtut. tn1.
-2 + 10 - 12
analytile sol et has quoque conditiones adimplere
iq
epsm 2 as. hol 1 tev 9 A C
(33) Nam 1.
fiet b1
Pone 41 =
F 56C50, 3176
64264 40eb
1949 2t0