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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 4
# Folio 14v, page id 00068217:0028
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X, y. 7. 5. E. B. ) M abc de
a. ab. abc b ali beq ode Thh
Mertious haec tenenda; quia omnes
a aequ X. a + 2 ab aequ. XX. Ergo a aequ. p-
ab aequ. y
ab aequ 7
litr
esentutus
ut formae quae ad alar invenitindlas naturagli ordue 
ab + 3abC aequ. yX ergo ab equ. y.
servire debent jam sint praeinventae, ita for,
abc + +abed aequ ZX
abc aequ ZX t
MVaebed serit ad inveniendu altiorem ejudemgradus
a aeq xpurg a t ab aeque Cy. x Ergo a aequ X 3yX + 3Z hac metrodo quam
a baequ yx 3Z ab+ D.
ab
abaequ y. ab + 2abc + b abcd.  aequ 1 y y. Erqu a b aequ. yy - 1ZX d
abc aequ. 7.
 Zy aequ. abc + 3a bed +  10 abede. Ergo a bc aequ. Z y - 3dx A 15(5E
10
abed aequs dyrego a b cd + 4 abcde + 15 abedef. Ergo a  cd aequ dy - +EX + 9 D
4 EX - 29
Ergo eodem modo erit
ab cde aequ Ey -5DX + 14 5)
Habetur enim facile progressu in infinitum ex ipsis nundiis combinatorius.
Notu in 
puncta a sinistro dextrorsum. in sequenti _ ert imtium l. 2. 6. 20. ilaai 3. 10. 38
aoc aqu. Z Laequ. abc + 2 a Bcd+
abed aequd dZ aequ ab cd F 3 a bide + Boabedes + 35 a bedesust tbabedesq
2
de
3Cy - 1B t DoBX- 705
1
Ergo ab d rgo 3Z  3CY + 5DX - 7 A 
Et continuando progressionem ... . ... Ergo ab ed eaequ. 2Z. 467 +91X= 16 
Hinc sine calculo per solum progressionis continuationem colligo esse.
Et sic in infinitum.
ratio
ab d’aequ 5d - 2EZ + 26y -25 X + 2n
abC de aequ Ed - 3BZ +5Ay - 7 MX + 9Y
a bc d’ef aequ 8d. qt Z +9 ny - 61 X + 258
Et generalis habetur regula inveniendi valorem cujus cunque formae ex solis t
literis quadratis et simplicibus compositae.
iam a ad formas qua aictontt )a pocedamus. legantissipo desriuntu
a aequ. XX - 2ysaa, X - r yr aego a + a b. erit a aequ XX yA +3Z - Exy seu a aquX. 3yX + 37. 
yX - 1Z
ab aequ 3X - 3Z , prX- 3Zp aequ ab + 2 a bi abe er it a b aequ y (Zx + 4d - 2gy
179- 4242 1Zx-95
abc aequ ZX - 4d    XX - 4d X equ. abet Ea fic+)a bed. hi abeagu z x- dx + 58 - 2Zy
225-6sx Y105 3dX - 15E
abedaqu ex- fE   dXX - SEX aqu ae bederabicdarabide. Eit abida P. XX. Exr6B- 2dy
Esy. B extis Ax B
Et continuando progressionem . . . . . . . . . . . . abedeaq. ExX. Bx F . 2Ey
at
ubi notari posse videtur rectius sae scribio aa
abx aqu. vyx - 2Zxx + 2dx aequ. a b + a
ZV. 3dX+E
abCxaequ ZVX- 38XX+5EK aqu abc + 3abe+ 2ab cd
eu
372 65y +bEK- D
a aequ XX = 2Xy  yX + 32
cb yx 2yG, - ZX +40
abe Z1X. yY- dx +5E
A aguX
et enite a 
X
Notetur egregius ille modus
a revocandi ad harmo-
niam cun caeferis dum
37X divellento in duas
partes = yx et - 2xy
nam caeteroquim ua hiutea
erat niadus series statim
L.4.d M. multiplicari
er 3. 4. 5 etc
os 22 40 xx ubi omnia eliganitissime destruuntur
ab aequ yyX 2Z +SdX - SE = ZY +4 2y. seu a brago 7YX. 22 + Sd X H 4y
abeu pz yX- 3dXxNIEX- 128. 372+4 8y
aby. gexeripd
abedxago Syx = 4C XXt9 B aequ abid, 3 alic abede abedaq Syk -rem 19dX. 21 A 3dZ+ 6Cy
2y52-9Ey + 158X. u N Drey-158X+ 41 1
Et continuando progressionem . . . . . . a bed eay Eyx - 3BX 19) X. 3 p 357188y
et omnino totius Algebrae clavem continet.
item
ut et in praecedenti,
idemque fit sem per
si progressionem
retro continuare velimu
ponendo 1 ante a
et a6 autea
item ao ante a
Nam pron
et
ab cX aequ. ZZX- Wy X pECX X - 26X aequ abC +abD  bEr qu 27X . d  + 2EL -R +36y +3d
abedk aqo der heyasdu rxe abcdiq abe e abie. Ergo erit ..... ab2da, in 3 + 14 mati 
add. gerige snige (ex. 8ds tibssorip
bC. Patet autem
facilius inveniri
forma
explicundae pet X. y. Z. et. ioeo jam in
et ipsae ja formae rjum indeta per ipsas formu
multiplicandi
valores per has eat
plus qum rectangulis seu formis simplicibus
ad quas omnia
redulere volumus
affinitatis
habet
abinitio, quod concoquere
non poteram
1
aZ. DIYX 5OX. 7A) aBC p. Z7X- id yE + EXX- 7BX 1Z+ D P, til
Nam ita apparet primum
X. y. Z etc. multiplicari per aseu
X 2G. deinde y. Z. d etc
multiplicari per X. denique