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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 3
# Folio 9v, page id 00068216:0018
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fine valde probabile fit, nullam inaequalitar ex a. b compositarum quan
titatum esse rationalem, qucur onim una ex aliis omnibus  quae ipsa srahonali
existante irrutionales sunt
jino hinc amplius sequitur. Omnem quate est ipsa
rationali cinsne gotsile et antia
ut et hujus potestatm
arcedeuta terzuliria c
cum a. b) esse irationalem, nempe ab vel dei hornti est irration alis
quae conferatur datae: a b
.fit Vaequ nge, seu n9 aequ ~ aqu. 1.
irrationalis posita ab rationali. Hinc sequitur
Puspiciamus nunc ipsas
A.1aequ. +S-g . - Yq aequ. A.
3 +A a +  B.
a apuA Bb agor
cucu
X 49 aequ. 0 Abriqu - 1
A+Baequ. 0. AB aequ. q
X+ 9’X - 17. ) qu q
BB) 3C) aequ. BR 49
(38 + (3C) aequ (A)
sa equio
67 bAa
 proximi praecedentis hoc loco secundi
termen factae ex hac per unam rudicem
deprissa seu divisa, et a secundotermino
D +A) + ECp + (3B) + 3BP  BC). X rqHL X + s+
(ta agu. Bs) e (BB
(46) -A N + ()
(C) aque 1 ) + (2B)
(b qib B). ()
(2A). (2B) sunt radices aequationis
gradus proxime precedentis hoc
loco sicundi factae ex hac per
unam radicem depressa seu
A Hoc unum ergo brevibus reassumamus
(2A).  radix quadratica esx quantibate quadam ratonali, aqua = (29)
(2B) aequ. - (2A) aequ - s- (192)
(3B) aequ. BA) +2A,  - Y. + Y
3C) aqu. - BA) + (1B) sn L Y ∞ Y
op) AA) + YBP +BB) + Y C B HBC)
(4B) aequ. (A) + (3 A) -  =V -t + Y, Y
(4C) aequ. ~ 4+ (38) =s -V - Y aY. Y +Y
(4D) aequ f19 + (9 -     Y 
GA) aequ. esCa P ACE) ei ap , la B) +. )C p) X VC) +  p +(2
(50) aequ 1 +A)  ail-Y
(5C) aequ. 1N + (4 13) - Y - - Y  -I. - d -J. ut-
1D) aequ 1) + (C) . . . Y ut -Y. it
V. -V. _ et
E) aequ. -(5 a) + (+D) -Y . - V. V. -. -d. - 1. -Y.
AB14)+ (a BV aqu
40)p 60 e)
divisa et a secndo termino
1) aequisx AeA) + 3(Z P + CB)
e g. 13a)
t quantitas est
(D) A
(3B) aqu . Bp +  2  sen -Ba + A
aintuum
sc 
397
(AB) act AD) aegu. (25))
est enim aequadio X + () + ( A) aequ.
pro B vel Cvel d.
pro (oe1 6 i X + AB)X + (B)
e coaqu. (+ Ca +) (E (4 ( A B)
G (AB + (C)
HA) q) aequio
LNeX MIXAequ.0
A (2B) aequ. (29u)
+BXIM +34) (X)  ( p3) aequ. d sit BX )+ (3 A3Xib g)
A X =Bqu) BA) + B r7) aequo
atdnique (3X) +(B1. aequ. o.  
1) (3B) +(3C) aequ. 8. B2BB) + 3A B3 C) AB B) BC ) aq. (29)
BA) 39 (3C) aequ. (3 p3) ((3B)H3C) aequ - (3A) BD BCuf VAy
(4XD) X + (Aqu (Y3) (X) + (454) aequo Ergo:
(AXI) +(AA) C)H (sX  + (143) i
a a Capust apapo a a B aquio
Cx) AtX Hy r C2aB) rac)e q
(n29 (4ABD LH. aiqu Ar.)
A. B. sunt radices aequationis gradus
+ABHC)(4D) aequig +g - r3)
lo bX)  Aui) aequ. 0. divitende per
(A + s B) aequ. d
A)) BaCr ad sago ( 4 A). (B g frB dHaB
loqu Cncclegolana getars aroeaie
10) aqu. ( pt s saej (cd aequ sases iona
XrgpH_Es Ex-Gteaquo et sAosBrS C+SDYsha
EXA +SAX +GAX +GR X + 9A
aatreusia n
i sa ois s re invi
 equ. ar. SBdCHBEq4
 unsre
 caneuotms
uutis e petrs propes ui til
SCago d scu s B.sA
A (+X) + (B) aequio (4AB) aequ (4 sa
e
irrationalium forma