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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 116r, page id 00068194:0231
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rerer
inus
consi
3C
eegouctcum quarandam origena
xempla Requationum de praescri
Ptis numeris explicabiliuem pro
singulis supra expositis Aequa
tionum Canonicarum speci
ebus.
Exempla suppositionis 1.
21 Z7 1. aaa 2 12aa F 47a -  - 60... a - - 3. 4.3
22 28 2. 2 aaa + 2aa +23a - - 60... a = - 3. 4
23 29 3. aaa + 2aa 2 23a - - 60.. a =
5
24 30 4. aaa - 2 aa F 17a - - 60... a - - 3
25 31 S. 2aaa2Zaa + 47a - - 60... a = - 5
26 32 6. =aaa F 12aa 2 23a -  60... a =
Exempla supposit.. 2.
22 33 2. 2aaa + 4aa + 17a -  60..... a - 3. 5
23 34 3. aaa + 4aa - 17 a .  60..... a = = c
24 35 4. aaa  4aa + 23a -  60.... a = - 3
25 36 5. Laaa 4aa + 47a - -60.... a = - a
26 37 6. 2ada F12aa∞ 17a . 60..... a = 4
Fxempla suppos. 3.
38 2. 3.5. 6...... ut in sueppos.. 1.
24 39 4. aaa 22aa + 7 a = - 60.
Exempla scoppos. 4.
22 40 2. daa 16aa +7 a -  60.. a =
23 41 3. aaa +6aa 27a - - 60... a =
3
24 42 4. aaa  6aa +23a - -60... a = - 4
25 43 5. Laaa 6aa. + 47a  - 60.. a = - 3
26 44 6. raaa + 12aa =7 a - 60.... a -
Exempla suppos.. 5.
45 2. 3.5. 6.. eaedem quae in suppos.. 2.
24 46 4. aaar 4aa + 7a - - 60..... a = -
Exempla supposit.. 6.
47 2. 3. 5. 6..... eadem quae in suppos. 4.
24 48 4. aaa 26a a +17a -  60...... a = = 5
3B. Tx hâc Aequationum communium inducti,
one manifestum est Aequationes Canonicas
Cubici Ordinis trinomias ab originalibus e
radicibus binomiis per genesim constitatis de
rivatas non ad omnes .. . . . . .. communes pos,
se applicari, dariq praeter dictam genesim a,
liam universaliorem e quâ tum hae tum alice
si non omnes saltem longé plures Aequationes
Canonicae ad fundamentalem es esse tialem-
Communium constitationem agnoscendam ido.
neae deduci queant. Vide. Har. Praz. Aral. Sec. 2.
aa ba +60
a LC
aaa t baa 1 bba
+ caa + bca +- bbc
aa + ba L- bc
a 1 C
aaa baa  bca
+ caa + bca + bcc
aaa + baa
F caa + 2bc. 1 bcC
Determinat.
b. +c
bCbc v
aa 1 ba + bc
+ b
aua ibaa t bca
+
b. +C) = 4bc H 2bc
+ baa- = bba + bbc
aaa + 2baa + bca
+ bba - bbc
aa + ba- + bc
a t d
aaa. 1baa t bca
tdaa tbda + bcd
aa + ba +cC
a +b
aaa  baa1cea
+ ba a L bba- L bcc
aaa t2baa tcca
+ bba- L bcc
lium. (abici ordinis geneses.
aa +ba + bb
a + b
aca + baa + bba
F baa tb0a+ 000
aaa += baa + 26ba + 60b
aa + ba L cc
a + c
naa baa +cca
+ caa +bca F ccC
Sectione 2.
Prax. Analyt.
traditam.