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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 18
# Folio 18r, page id 00068231:0035
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januar 1679
Sit aequatio
X
1)
+
1
qX + YX +5 aequ.0
ponamus X aequ b a + b +c d
V aequ. ab + ac + bC
Z aequ. abc.
Ex aqu. . 3.  Habentur aequationes: a ae qu. X - 41 X + 4 ZX + 29
ad aequ. Y - 4XZγ + 4 y +. X72
674
Vide Tabulam nostram
datuoet ae anqu. X 8y X 15Z X + 10y X  3. yZ X - 16. 25 X e 1 Z X raYZ N . 87
b
ope duarum aequationum 5 et 6 tollenda est incognita y. et ad commodius
tollendum usui credo esse poterit aequatio 7.
loco aequationis 5 scribamus compendis causat eXyyeg
NI+ exy + fy +gX + h aequ. 0. et loco aequotionis sex scribemus
V+ lXy+ mX + ny+ X aequ. 0
sequatio 8 multiplicetur pere foriulam X+ X(3XBrAXy
+6yB, t2
10)
 ecCcC
per forimulam: X4 2X, 3X  14Xy+5XV +6X∞+7Xy18X)gKYX nX
+ 1XY + BX y +1y + 15X +16Xy +17Xy + 18y + iyX + 20xy +21y +24
+23y +24.
In qua formula omnes sunt termini ex X et y compositi
qui non ascendunt supia gradum octavum si pro y ponas liq
alriq aliquod quadratum vel rectangulum.
similiter aequatio 9 multiplicabitur per form sequentem
11t
formulam,  X +31 X3 + 32 XY +33X + 34XY + 35 Y 136X137y138
in qua formula omnes sunt termini ex X. et y compositi qui non
ascendunt supra gradum octavum. Si pro y ponas aliquid quadratum
vel reclangulurm. Et habemus utbitrarias ex his aequationibus
numero 31 minimum
(12)
Componantur jam productum ex 8 in 10. sit form. 12. et productum
ex 9 in 11 sit formula B addantur simul formula 12 et 13
(14)
fiet formula 14, quae hos habebit terminos:
Xe. X Xy. X Xy. Xy. X.  Xy. Xy. Xy. X. Xy. Xy ~y.
XV X. Xy. Xy. X2p. Xs Xy  X Xy. Xy. X y3 Xy XV y.
x Xy. X y. X y3. Xy y5.
X Xy. y. X. y. _..
X XY. Xy. XY. VI X. Xy. Xy y.
qui ubi toltendi sunt omnes
Termini, in quibus reperitury. qui sunt numero numero 36
cum tamen arbitrariae habeantur e tantum 31 sed hic
succurrit aequatio 7 nam quia ejus in que habetur valor ipsius
V. ideo ejus valoris ope tollentur omnes termini quos ingreditur
V qui sunt numero quinque scilicet Xyt. Nyt X est Xy. 
ristant ergo tollendi termini 86. 31. tot quot sunt arbetram
arbitrariae in formula 14. Itaque superigit tatum
aequatio loco formulae 14 quae ent formula eag quindem
nempe in qua restabit X
jam aequatio 1. multiplicetur per formula Xd.... erc. ut exto
tetur etiam ad gradum 12. quae formula 16 erit instructa 
arbitranis numero 8. si placet B. cujus Tonnini comparandi
cum terminis formutae 15. itaque opus duodecim arbi. productum
ex formula 15 in fotam aequ.1. habebit 8 vel 9. arbitrarias
et 12 terminos comparandos, cum 12 terminis fomulae seu aequa
tionis seu formulae 15. itaque hac comparatione invenienturtum
arbitrariae e vel 9. Tum valor quantitatum a +b+c. et abhat
+b7c2. tum denique, vator quantitat et abC seu Z. Quod quaelebatus
datur et alia in
qua est ab aqu
 23.. V. ea
cujus gre tollipotest
nsi er p
prater aequ 5. b. 3