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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 230v, page id 00068201:0460
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si prima illa scheda Apil. 1675. tol. de excitationibus aequationum resumta fecissemus:
poncndo X H d X + ag et ut supra fier:
d X2 + 4d’ag X3 +6 d aegr X + 4 dag3 X + at gt
d’o ace
2a tast..
4dag’ac .. + ag hac
4bd af +4bdague 2ae
+ b292 2avaf
4baep ac 2677 a 2 ac
+b daque aat
ac  fei. (4 . X7,  X Cd ac X + ac
Sed non opus est aetra progredi, jam enim video nihil esse quod
= b d. +2b dague. +. 69 a
prohibeat -ac +ae +a taf haberi pro una eandemque quantitate arbitrariam ita non nisi duae
prodibunt sic arbitrariae, et dici potest: A Z sac Z + a β. et ga Z Z+ - 2a2Z + a 3
-+ac
et explicando modo supra dicto:
ap...
+ 4dag X
+randaue
2 an bd2
+ 4 aeb...
+6d’ag X + 4 dagX + a  9Y
+ anag
+a anbdaque
+ anbd
+ baeb
iam. X) tahi X
+ 2anbaq
+2 anbdaus
+4a’ eb3
d+ + and + ae
+ a l X +aemb
+mah.
erit mej 4d’ag + 2andus + ranbd +eb Ex collatis terminis secundis;
Et ex collatis tertis:
de + and + ae
er d ah + and ah -6d ae g - a ng - 4an bdag - anb a
6a3b2 = ah
Rectius contrarendi culculi causa ita pro cedemus. Quoniam ostensum est omnia problematu solida ad radicis quadaerae extra
ctionem reduci: itaque simamus aequationem culicam puram:  Y + al pjo. et ponendo y +, PX +  ah
tei 3 et P X + 3 p  + 3 pati X + ae h
Xh + 3gX + 3q X + q3. Uende aequatio: X +3paL X + 3pat X + a (3
X + 3p ah X
Multiplicetur aequatio producta per X + m, fier:
+ 3pate X + at3 X
+ 3q a l ... + 34a l.. +q a l.
m p2...
+ mal..
per terminus tertios fiet: e
3+  x, 23
+ AMpim 4 amB..
+3gal
p + ael
mqe et) Has ergo duas quadrato quadiaticas aequationes B er
3Mpah. +mpati.
+2mqa l.. +3mqa l.
33 + at
tq’ac
sro conferendo, opusnascentur collatitiae quatuor, sunt
autem arbitrariae numero novem, scilicet, n. P. d. 9 b. m. ph. 4
ah d4 = 4dgg 2p
per terminus secundos fier: ep 3Ga l aud Eandaue al 1 abp + 4a bael
2anbd2
3a p ah. 3 aqu l (amp a mat
Ut calculus adtie minis protioque magis contiaatur loco aequationis X  3pt at, X ex. ponemus:
X taB X +  ad X + aB A0. unde multiplicando per in Xam fer:
+ amd  + am D SH.
 ponendo scilicet hp aB- 29al et q
et oa    ba al + 3ff99 a 1 + 3919 p 7  59 pt 
cujus aequationis ope, haberi potest q
itaque quoniam sumtis pro arbituo β. et 8. haberi possunt h. et g. pure arbitiania seuper et aequatione
aliqua collatitia
determinatis, et seu valore ipsarum β. et d. pure invento, valor etiam ipsarum h. et 9. pure
inventus est. itaque ipsis β. et d. uti possumus velut pure arbitraris non minus ac g. et h. Reliquae autem .
et A. innveniri ab imitiliter inveniuntur absolute. Quoniam ergo aequationem D. contrasimus, contrahenda nunc est
etiam aequatio O. et pimum C 4 dag 1 randag + 2a nbd a. Imo nota si ingress in progressu
inveniri posset (3. sine B. itemque d. sine D. tunc pro absuente mientis poterunt haberi, h. et 9. Alioquin inbiliter
brachulogia erit, utilis quidem ad compendium calo compendium laboris, sed non ad compendium inventionis. Nam in fine
denique ad eas literas explicandas redeundum. Aequationem O. ta scribemus. X+dag
X + +dhag X3 +6d ag X2 + 4dag3 X + a 94
tarn
+ ba eb
+ and + ~C
+apn. +abgan
+4eb. +aeb+
Nunc conferendo  aequationes () et )Otuto
70. licebit invenire b ipsas n. e. m. ac proinde omnes
evolvere collatitias ad ultimam usque. et primum ex terminis
secundis fer: 4d agot + a8 2n + 40b  e - d+ a B-adaβn- a  m
et ne ad d3+ 5 a )- 6d a9-6 a’ eb l 7 4d’ agotaβ. a2   a b tea p ad a(5 B
+ d4) + and A+ a’est
at rN- aad - aG A a β + ad aB aB + a 3 aB
 ratas = 2actaf
d X + 2dag X + a g2
e b X + b2
d’r + 2dage + aeg X
zac laf
+ 2b... + 4 bdag.. +2b agX
s-q ul
d. . 9. 6.6.
p’a5+ a
sive - 2a l - 2 a  p
1- a q’a P + al9p
+ p a + a lp
et paegalo rjala atrga
unice utile
genuoqus