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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 16
# Folio 17v, page id 00068229:0034
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Remergo ita rassumemus:
Aequatio proposita reassumatur pro , substituendo
hl sulstituende aquationis propositae: In- 15  M
Ventelur diuisio per n3 - 13
pro 1 h substituatur Vn + Vp
fier m
15l m
set fier co
2 4 (24 0.
+ R1
Inde aequatio inter
An ergo rectous ita:
confeenda cum 4
= 4(2. p0.
-u q
Pone quf ex postenore
Cm co confeaenda cum M -co m + C +2
1912 (1f- 8, ef  - t
(c0) - 2coV- V
Sed restat invenienda T.
nt - 1 tlso  + 125A +af astt 1 196
lf.
49D 19b 7  ayo
+ 30(37
+pZ20
.... + p
sideo Determinationum obtinendarum causa, rectius rediri ad aequatio irrationales
Igitur Una determinatio est:
M p 4 ml + - b.
508
Altera m Y X + 1s P M + 41
Igitur si arbitraria M, talis sumatur
ut quadrat quadratum ejus vel quadrato quadratum, his quibus majus esse debet, sit
aequale, erit valor assumtus omnium possibilium minimus vel maximus
Ex prima aequatione fiat: m - 4l M + al , 6C fict +m +2l p1S6.
sive M p + l 56 + 2l, seu m 1o
es
qu 4 2 5l + 41  10l425 (2
Altera aquatio dabit. M+ -   M + 225 lt  (225 (1 4 1t2 18) 3372
Ego i m () c
5337
Ergo- n  (4) ( Sor 4 15V et m, la(CH D So +15
Seundum primum requisitum, ponamus M . El fet 25 l 6t..  in integris valor 83 4tor
ipsius m, omnium possibilium minimus affirmatious est 5. ponendo 4 esse +.
Utemm autem nunc quidem affirmativis ne in novas difficultates incidamus:
Altera determinatio dabit hanc Aequationem:
Ergo (F) m (+
) 15(a
m -15(V + 225 (4 ( 337 17
12 520E, sive m 
196 195
(3 + 151 Qui ialor est omnium
Et  quodratoram possibilium ipsius m, muximus est omnium possibilium maximus, nam
quadrati
si sumatur major tunc valer ipsius m, fiet major quam 15 l m  4(+ Certum
Habemus ergo 15 + 18
133 12=. Contra ut vulor paulo minorem vero minimo.
+4 +4X  eberXa ex  78
Est ergo maximum omnium possibilum  2 L, minimus omnium possibilium 3, quod est absundum 141) e
pondo exs 1. fato a p +X pls mistrore pu x vats ratim propposica a mim. Cxteu Epline prats
= 16 minor quam, 3, ponamus quod maxime, favopabile est, esse 3, ficta 10 - 263 21) E
solutio ergo in numeris ita ut omnes ores fiant affirmativi est impossibilis.
9 2i
duo nequadralorum quadcuto quadiatus a a +IH, a + a+ 2al +  seu 2a p2a l(7
mmeri unitate differcutes ita ut lun
9 a
Jam ut inveniamus minimum, ex quantitate 10 + 2S5, faciamus: 1a - 250. Est autem 1.B
14 1 14
enim est, si valor alicujus inde lateris angeatur, augeri etiam valorem  potestatis uto maji 269
fit autem maximus, explicando (4) pere pe +, pono 5337 est proxime in in tegris 18.
225 4301
51