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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 367v, page id 00068196:0730
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ili sit dy: Ax = h, et X: a = m, et y: a = n
seu hamin
habotur aequatio ex h, m, n. Et simnl datur farcenta
rationatis Quod si _ habeat valorem rationalem, datur
l
v formula ex m et ni
sit m Pq et n = p 9
et subsituendo et tollendo m et n exaeq. 1 per aegg. 2 et 3.
AH
ia i= piql  posito Redari ex p; 4  p; 4
omnes evanescente q Hoc si paeplani posset haberemus
quaesitum per praecedentem staginam, ponamus
et rursus alium valorem ipsit 4 quaerendo ex2
 X
et 3. quia h amidu  seu = p p: 9 per
H C7) X
1iq= Pig
quae aquatio eo reducatur ut
sint tria Z. v p, SZdo- vazue : co0 24, et Zd0 - vaz:   Y
1) 
formmla generalis ex tribus M= p; qr rationaliter integre
n = pi qir ravaniter integre (id enm in Trubus semper licet salia
H
gneralitate  ut puto) qui valores slectutum s dm: dn
Ergo in an: Meldur evaccescet differentialitas restabunt
tamen duae summae seu tres qu numeri, p, q,r. et fiet
an: am = pi 4;r =h, nam hest duidur ut patet a
CA 4X
ex intio positis.
Purtus in aegu. 1 pro mn substituatur
I
valor ex aeq4. 5 et et 6. fiet h = p. 4
 (91 Au
quae duo
aequardo ex 7. et 8 fiet piq. r = piqir ubi evanescere
debel aliqua ex literis ut qet fiet p:1
Unde
Ex sequitur dari posse m asse (per 5 et 10) in exsol qir, et
n ex solis qir, adeoque et hexsolis qii; et quidem bis,
ex 7 et ex 8, sed ea coincident inter se
si expliantam
conferamus acont aeg. Cau ag. Z pir 72 23 ( a 462 90 n  61 75-
72. 73aa = 89 - 2. 6,4 2.73. Baa = 88 26,  et equando 2. 61 fit 88 - 2. 75. 13a- d9 32 3a
Confenm ob XyAX et Xdy patet fore 87 = 3. 89. rursus 561 = 86 - 72 - 2.  = 3. 99 - 3. 72. 13.
Ergo per aequ. 3 et 6 habentur 72,73, ideoque H 61. per Xaxet Xdy d habetur 6 et 71
comparando x du et XydX fit 83 = 2.85 = 3. 61 71 aa +4. 61. 73a et quia b1, 71, 73,am,
habentur, itaque hinc habet et 83 determinatur per 85 et alias superiores. 1
70 habetur per Xdx seu per 82. jam 81 = 82 - 2.70. 73.1 70. 75 + 2. 60. 15461. y p (C
2.61.734 61.72a
denique 80 = 70. 71 a + 268.61 + 60.71a - 2: 61. 70a
si hanc aequa tconem C comperrium cum aeq. n vet 3 iusleda disferentialir quabis xer ad BX Port e 
2o1 3
determinaves tantum quieam in a. C efficienda. Nam in calculo peculiari pro, hac aeq. D reperimus gb3. 89
ob priorem fier: 372. 73(4 364) 
(72+ 2.73(+3.64W
ob posteriorem fit: (2.72. 732.60+ 2.78643) n
2. 73 = 72. 73. seu 728273
4. 73+
 quo bulore substituto in aeq. 3 sit
quod succedit feliciter. Restat jam uniga aequatio
t raari - 2a415
+2.617 -26,4
ex explicatione. sed ita in
idem absurdum recidimus ut scilieri
tam co quam  dentur ex X+G, si sat
72=3. 93. itaque impegimus in scopula
quem vitabamus
98- 89. 82 -31 quae proinde etiam succedit, ut patet (einus disralis est. 91q. + G2Xdy +293K 794X) L4gXx ib Xyly 13.91X X97Xdy + 4. 98X x = 0
13
87
omnes literae
praelen x, y, 
sunt rationes an
quanttates
2. 89 gC
est habetur ratio t72: 3
Ergo fit
B. 
34+85-83. 2.85-83
er1. B43. 71. 13a - 62. 71 24. 12a
+650.61 +606) ∞26D 6( l
(+2aa. 61. 13 +a. 61. 2.73 12. b1. 2. 13
=244. 61. 73 a1a. 6173) 4  2 651. 13
P. bie3