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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 187r, page id 00068200:0375
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conditio deest, ut ad daas aequales
radices determinetur, toties duo maximi incognitae duos aequales valores
l habentis, tolli possunt ut esto aequatio X +BX MaX + nae X + ple ro
determinanda ad duas aequales radices: ergo
et jungend prima multiplicatio dabit.
17
+ 2ma X tna X + 4pa r.
4X + 3lX + 2mak + na 0
Ema X +3naX + apa
 ma
nar
10.
In aequatione alibi inventa circum hoc problema:
v
et pro p, ponatur 15 y, fiet s -y
sive ranco
Et pr fiet:
sy
 axfax pat
uq
  +I et So
++ yf (+ +) XX
d (+ +) .
 pro X + P, ponatur V. quam V necesse
m7
2
posterior dabit.
Ergo
Elegans satis observatio
de (
Jyp
(1DYf (t F) yx.
45a = 29x f + y X
Ly+ 12dy + y
ax
C
reddendo
tso
 Et pro 5 =y ponendo B,
rax +aX
pro V ponatur ejus valor fret:
de ()  Srax + ax et qdrando.
++) f(t) X (+ +) p
(
est esse eanum,  et
possumus considerare velut eandem, etsi quia puncta A. et P. immobltia sunt, utcunque duo
sint puncta X et Y quare ipsam p explicare utile est, est autem pa + a X fiet:
da + dax
sI
2ax  a e et quadrando per 15-y, fietus.
Nimirum FPp, (+ +) ((+ +) W  dSo-
(+ +) F)V dssE
(+)
-dse
haec
aequatio tantum unam habet incognitam duarum radicum
as
Lis
dgu sive
1V -y
10. conferitur cum simili duarum gudicum aequalium Y y, e y -Y
2+ W + d
 multiplicetur per y + mconferenda cum u- re +C
I locum X, subpiluatu 2ax f a X, fiet:
Nry
+y
ytyrys
+ +29 X + 24d15 un 510.. juio nondum conferri potest, qua
+d nondum satis deterim nata, est, u nulla atra
a
restet deterutnad quam ad duas aequales radices, pros, substituatur ejus valor petgr
pro p, fiet a 4 2a X + L X et pro y, fiet 2aX + a X sed nec sit procedere
puto quia ita mimium determinationis affumtum est, videamus tamen, videtur enim in nostra esse
s
potestate, vel s explicare, vel WV:  Ita est, sed non debrisset puto explicari p.
An sie, habemus. Venit inihi in mentem res notablilis, nimirum aequationes simles
comparari posse, etsi non sublatis signis radicalibus: ut ecce aequationem superiorem
2d rax + ax  +ZX  bX + ta. A10 si jam alia indeterminatu, duashabens
radices aequales similis propositae haberetur comparatione facta solvi posset problema
licet non quadraremus aequationem, quinqe cule coleatitios adert tubus opus incopuitis pors
El