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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 282r, page id 00068194:0563
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octobi. 1674.
schedinemdram constructione per
transform
aliqua curva: cum tamen non minus commodum sit poblemata solvere ope rectae
et cujusdam bniae, quam ope circuli et ejusdem.
5V
V n aXy+ V
n bx + c
 Esto aequatio cubica: V +lV +maV + a n r o sit  sm pplana
Hec aequatio tot modis divelli potest in Analogias, quot habere potest  modis abire in
aequationes differentes, mutatione signorum:
VV- may- an hine nulla
F analogit, nisi adhibita unitate constante, nde, quae in varias dimensiones pro lubitu
Faltolli potest, inde fierieum polunt: e A - 147 - may- an, unde:
 I
-1y = may - a n. ul ita: y = là y ma y - an sive
-
Eodem modo institui possunt diversae aliia divelsiones
in analogias, quas ordine omnes enumerare licet.
 - n y - n.
Vinc ad aequationem ad rectam: ea este vel e+ reb +bpo
a
ea est  + e p = Y + d,  vel E p c y + rcd y + d
(+)
vel e  e + (fy + g,70. sive e + refy + 2ge +f y +2t gyis
aopaciones
5 quas jungendo,  et pro et, su in  substituendo ejus vatorem ex 5, fui
Cin speciem
vae ante
75.V 1 4lgy + f9 + fet y + fge 70 e
di sed divisis omnibus per FY + 9, fier: fy + g + e ad lineam rectam, ipatet
X ergo simplici multiplicatione per quantitates arbitrarias, aequationes ad lineam rectam
icomnium formarum reddi posse, ac proimoe fieri posse, ut aequationem ad aliquam ad
+ Circulum, aut Parabolam, aut ad altiorem etiam lineam esse credamus, quae tamen
Ai ad lineam rectam, aut aliam, ea quam habet specie inferiorem. Interim
 videndum est an non haec ad speciem parabolica verae locum supplere possit, in
e
30, eo quod cum alia paratilica om vera composita, ex hibet aequationem ad
 Circulum. Esto jin aequatio ( (7)  -  +yp ad
PF 5 Inde analogia: (8) a
 ran pro y ponatur ejus valor ex aeq. 6,
=P.
y- agay - 9 a - easy - aq e et exaequ 1 fur:
S1
 ex analogia 8, fier: (1
s
af
+ac
2gaf y- ga - af e age asti ug
. 195 y - g’ a - f et -age 1)- L- py
Sed jam video in quo pecaverimus, mnirum aequatio proposita 5. ne inspeciem quidem para
a
bolica est, quia in ea ducitur, una incognita, in algam, An ergo ita: aequatio-
nem 3. multiplicemus per ) el- dy + tpo fiet: (12) le-f ly, +gel- 9fly +hg
+h. ha ilia ad parabo
tam per sim plices multiplicationes aut etiam per compisitiones cum solida Uenum tamen experiendum restat
sunta analogia aequationis subiae: ) a V ayn et pro y posito ejus valore ex aeq. 9. vel in honis ut
tantum, vel aeque in nominatore ac nurhrala
on e ul es  
n  e d slienti airpita ce ag. 12. 282