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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 28r, page id 00068200:0055
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(11) Hinc inveniri potest quid sit rationale in ae, et
a + b + C+d,  et in a+ b + Cx ab + C + ad + bc + bd + Cd
et in abc + abd + acd + bcd, et in abcd. Nam scitur
quid sit rationale in Exempli causa scitur quid sit rationale in a per artic. 9
enqu quid in aa + 2ab Ejus sed  scitur et quid sit rationale in aa
Scil. tantum quadratum rationalitatis in Ba. sed scitur etiam per artic. 9.
qud sit rationale in aa + 2 ab Ergo habemus quid sit rationale in ab
Hinc quia jam scimus quid sit rationale in at et in ab, et in a + 3 ab +6abc
invenemus et ex rationali in  scrinus inqud sit rationale in
 et ab scimus quid sit rationale in a, et in a per ab
facile habebimus quid sit rationale in abc. Et ita porro.
Hoc etiambrevm, quia habemus quid sit satiodle in a,
tl Ergo et quod in a, et quod  a
Hinc etiam inveniri potest quid valor ipsarm
iat quantitatum cam positarum seu formarum simplicium
(12
seu combinationum a et, ab et abc et abed.
Nam vatur quid in lis rationale per i1. sed tota sunt rationalia
quia a, b, c, d sunt radices aequationis rationalis
art per artic. 8. Ergo habestur ipsorum valores.
Habetur ergo a, vel b, vel c, vel d er
seu h; vel lvel m vel n per aequationem
13
quarti gradus;  per  artic. 12.
(14) Ergo per mudam extrtio habetur valori
ipsius X purus. Nam habetur ecl a per
vel b vel c, vel d per aeq. quarti gradus. Habetur
Ergo pure quia pono aequationem quarti gradus jam
esse resolutam. Ex hoc valore si extrahas radicem
kit.
puram Sti gradus habetur h, vel l, vel m, vel n
adeoque X. quid
e
quod desiderabatur
Hypothesis autem articulorum
e
est in potestate quia regularis ex
eo ipso quod exitum praebet