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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 287r, page id 00068194:0573
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Resumonus ergo. Aequatio factitia data est: V , . DB . gaV  qa 16 a 
Aequatio data quadrato quadralica: V IV  am V taenY + ap. 0.
a qua sublito secundo termino, Scribemus: 1V4 X + a WB + ae ZW + a51. 50
et reducendo ad cubicam, + + 2t 7 L= 1a 7 27
a
272
=a5, et opuendo  e7 F  fiet
fiet aequatio culica talis: 5 + .75 +  2 5 - a X r
et sublato varce termine secunde quae cujus radices ita nultis licaui possunt, ut unam habeat
cum factitia simili terminum communem. De quo postea, nunc teutare operae pretium
duxi facillimam omnium madhinationem, secundo termino non sublato: nimirum,
habemus: V3 + . 8V + 2 a V + qa V + 6 a H 0, aequationem factitiam
et Y. 1V nam V + anV + a  e 0. aequationem datam; ponatur V p Ny, tiet
ex aequatione factitia: X Y + 2D A  + Y a X + 9a s y + 6a 
0a
ca
rai
divisisque omnibus per N fiet. yt  2Da V3 + 2aa V 9~ a 1 +6a a 
ar,
Seo
ox
ON
93
 am, fiet s a . sed parum, hinc, opinor, incris
ponanus jam s en vd fiet NV + 24 ~ V 1 7 2q B - a d et
divisisque omnbus per N, fret: B2  14 a B +
a
ponatur dacta BX + CX r ha, fiet: aequatio factitia ) X - 1VCX 2+ Y S X + C X  e) Aequatio factitia. V + 26DD + 26YV
(N) C
+ ya
X q
+
a 
40 3 
V- 42
N3
(+ . D8  p
Fo Z-ava
oipa 1) Far crm
0 (1)  O (7)
conferenda cum 6V + 8 1V + oan D + n D + 02 p p o
Enit DE Olatemt QB Oam D + Z  E tem.d. 1  n + 8 Y  Extem 1.
d5i cteg1.
aq. 2.  28
Aeq. 3.
tuea p +07e,
ponatur Q 1) e P, siit ex terminis altims Ay e B - oan + ar cn si o p
vee n e + a + 4r q  =  ap, fietue: ex terminis quartis: 2V4, + 
in quacto termino factitico reperitur n, cujus valor substitut ex quinto, ubu
0ya e can
et ex hac aequatione crit: Y  2F +   a p an
et supra
pa
Oaen + aD
tea +o7n
oa + aron
sed ut rem rectius complectamur considerandum esst
a 8  a= 8r y n ( 207- ’an ex teminis quartis,
et Bxa + 8r 1B a, B f- ap +4r q . Ex teminis stis.
Ergo jangendo   2DZ - an M B F O a + aripes et pro   sulsti
tuendo ejus valorem exterminis tertiis, fiet: 1DY n-C anp  4 - 9 a + O  B = Oam 
ilem jungendo duos alsolulos psius e ontre, fret.  6 an + 18ha + 4
en
rp 10Y +7  20 710 an
+ba + e