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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 7
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Utile autem erit commemorure qua via ad rem penitus
ernendum excitatus sit animus:
in duas aequationes ejus modi:
2N 2E
X
Incideram aliquano
n + n p b et memuri
Fy 1Ab et XY B acc e quarum altera est
circulum
ad  lineam rectam, alterm ad  Hyperbolam cit ca
alymptotos. Unde sequebatur:
et yt -Oy + ac. sive
et VH 16+ 5-.
Xp) a. adeoque dc +y  b
V H + + Y -   tE L-3
 Ergo pro X2 + y ( b.
ergo substituto valore ipsius y, Scritebam
X + b + f- et p b., sive X1 Yb - 1b- c
 Erat autem C major quam b, adeoque Sb2 -e erat
At vero
et aequacuidam linea a
in quod me valie serplexum rediidit
praecedenti
Cum enim ex calculo praesenti deduxissem,
TX + y + ~ b + 1B - c + lb - sV 2, non capiebam,
quomodo ejusmodi quantitas posset esse realis in qua exprimendam
imaginatiae imete sive impossibiles ingtederentur. Relegere ergo
calculi restigia coepi; errorem suspicatus. Sed frustaa: e eadem
enim perpetuo prodiere.
Tandem venit in nentem calculum operationema
instiluere quam hic subjiciam;
d
P3
b + 16 -c + sb - sb
4
Ergo quad rundo atrobique,
+Fb-e + b + e, = sie dp, A+ B. Ergo quadrande utot
aeque d  + A2
t
5.t
ub + 
rectungulum
+ Be
b - st .2
+ 2 AB BIBLI
+ 2C
ipsius d, fiet:
mam
ac nenerre 
erit ergo ergo dp b +2c adeoque
Aeqtando ergo inter se duos valores
 b H b. + -C +  - 1 
BLCa L A
comecio ed
Nam (AB, sive sb + B- et in SB  E facit c
it calculus ostendet.
a p)
une
Yb+ 2C
stende si in numeris faciamus  b p 2. et C etiam p 2. fiet:
n se
 Y6ni
Si + s- 3 + S1 - 5 - 3
Servation farite
Qua Therremate nullam in tota analytica singulare
natatam
magis et paradoxum a me nemini est egrvatam et nam me
primum me arbitror quatta pi  radices irrationales
in speciem imaginarias; adreales etiam sine extractiones reduxisse
aes
Er notabiles iest, no sextum nos habituros Operationis sive
grithmeticae hoc analyticae genus; nam praeter additionem, subtractionem
mulsiplicationem, diisionem, radicum extractionum habebitur Rednctio Reformatio le
Reductio.
deu pares so tolun Additio et
v
subtractio composita reducunt ad simplicia; multislicatia mpliita a
expressai Multiplicatio es causas ad effectum: Divisio et extractio contra-
Divisio fractos ad integros. Extractio surdos ad rationales; e denique
Reformatio imaginarios ad rationales reales.
Cincognitarum XtX
aB