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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 282v, page id 00068194:0564
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caeterum quod de aequalime adlineam rectam, id de aliis omnibus tiliter observari potest in
aliam formam redigi per multiplicationes
Colerum si aequalio duas habetradices aequales  facle ope lineee rectae id est tangentis tantum
ducta de solvitur problema: videndum ergo an problem aliquod per Tianeformationes
ouipere possit duas radices aequales: Esto aequatio: duarum radicum aequalium.
V + 2ey + e. Multiplicata per FY +g. dabit, s y +refy
Esto jam aequatio cubica data:3+ 1+ Ma3 + anv.
c6
Unde pro Z porendr 2y + _, coit Z2 f
dhoidendo aq. 3. per ta, fiet:
et dividendo aeq. 6. 6. per
1Za P
ma
+ a
23
sunt autem collatitiae tres indeter
minatae Quatuor, b. c. f. g8 uria
Vy + 26c y + 3b5 y + c
+ 2ed
2, fier. (8)
+ e V
+ a.. C + 2age- + age
37 + 1ac7 + 3ac y + (et
+ la .  il a c. te
ergo videtur supernumeraria esse, quod videamus,
fingendo interm c. Sed tam bideo non esse nisi
e quiaq semper sunt simul, et proinde
 aita..
unam repraesentant. Ex prima collatiia. ag  3 ac + la e
ex secunda: rosacet ilae - (90 p 3ae + Elar dm (-)
et extutia. C hac + la 5 - 20 a
per ac
13
b.
17 b3
bne
enc
Sr, Aer. (1)a e , lacc- e ac  a 0 + 21ac + anc
3b
b
62
363
(x C3, in aeq. 11. substituendo ejus vatorem ex aeq. 12. fiet:
Bace + la c -2e L a3 a 10
od
36
1a5 e + 2laeec - e’ac = r la - aem C
B binc F
b
3b
elidique poterit ipsa _ c. Restabunt denique inncognitae duae, C, et b. quarum nentra
amplius elidi potest, eoque casu videndum restat, an possibile sit ita explicare unam ex ipsis,
ut altua plane vel saltem pure habeatur.
+ 1.
158y
+g.. +2ge
+2lec. + 1c
bn.. + bme