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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 115r, page id 00068194:0229
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quens
10
Frgo coefficientia e homogeneum datum propositae coefficientibus dt homogeneo dato
Canonicae in excessas ec defectus habitudine contormia sunt:
Scent igitur Aequatio proposita e Canonica aequipollentes aequali scilicet radicum-
numero praeditae.
Sed Aequatio Canonica de Eriplici radice p. 9. r. explicabilis est.
Explicabilis est igitur Aequatio Communis proposita de radice triplici, uet est
enuntiatum.
X1O A.
Ex Demonstratione praecedenti manifestum est AEquationem communem
- - - --- aaa - 3baa + 3cCa - - + ddd... in quâ.
C
= vel L d........... Requationi Canonicae supra ex positae non esse
aequipollentem, ac proinde de radice triplici explicare non posse . . . . .. Unde pa-
tet condetiones  ab Harrioto expressas nempe b. = c. et b = d. non sallicere ad
arguendam Aequationis communis propositae cum superiori Canonica de tribus
radicibus explicabili aequipollentiam, iisdem enim manentibus fotest esse
C= = vel = d. -: . - - Secus in nostra suppositione, inquaposito b = c. EsC= a.
necessario quoque est b = d. adeo ut duabus illis conditionibus positis haec tanque ne
cessarium consequens omitti possit.
Exempla Aequationum in quibus
b = c. 8 b = d. e c = -d.
1. aaa- 13aa + 48a -- 64... a -
2. aaa  1416 aa + 48a - -64... a =
3. aa a 2 6= aa + 12a - 8... a=
A. aaa = 93 ad. + 12a - - 8... a=
Exempla Aequationum in quibus
b 2 c. e b 3 d. e c L d.
1. aaa 10aa L 12a - = 27..
2. aaa 212aa + 26a - - 60.. a
3. aaa ~ 12aa + 16a-55... a-
4. aaa - 18aa + 35a - - 48.-. a
Exempla Aequationum recipro
carum in quibus itidem b = c. et b =
esC = d.
1. aaa2 6aa + 1a - - 6.... a =
2. aaa 2 12a a + 5a - 60.. a
3. aaa 212aa + 4a - - 48.. a
q. aaa = 12aa + 3a - 36... a=
5. aaa r 1Zaa tZa = 24.. a-
6. aaa r 12a4. + 1a = 12... a =
a
e
12
12
11. aaar 18aa +7 a = 12
12. aa a r 18aa+6a -
13. aaa 2 18a4. +5a-
14 aaa r 1844 +4a -
7
15. aaa 18aa + 3a - - 5
16. aaa - 18aa + 2a -
17. aaa r 18aa + 1a -- 13... a
1B. Hae 17. reciprocae Aequationes aequipollent
huic Canonicae reciprocae de radice simpli
ci p. explicabili. aa a r paa + 99a = - p99
ret enim in
hac est . . . - 99 -- p99... sic inaequation
nibus quoque expositis singula homogen ea data
constant ex ductue coefficientium. . . . Qvamobu
rem si in Aequatione communi praecedenti.
aaar 3baa + 3cca - t ddd.
fucerit. . - 36)- ddd... ae quipollebit.
et d Lalblucae receprocaenipsad 8b. em
racix dequationis Communis proposctae expli
catoria radici a. de quâ quaeritur aequalis.
Vide atuer 6. prop. Sec. 2. et 18. prop. Sect. 4.
7. aa an 18aa F 11 a -- 198... a = - 18 Prax. Anal. . . . et ea quae paulo superices ad
8. aa a - 18aa + 10a - = 180... a = = 1E
9. aaar 18aa + 9a = - 162... a = - 18
10. aaa  18aa + 8a = 144...
Vietam de ambignitate Cubi multipliciter ad.
fecti annota sunt.
Definit... .-
Sec. 5. Pras
Anal.
Proposit. 5.
Sect. 4. Pr.
Anal..
+Prop
Sec. 5. P.
Anal..
0
d
e
1E
3CC
36.
Proposcta Requatio de