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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 447r, page id 00068196:0889
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Mocnta generli omnium curoum exs ordinaturum expressioned, puta rationali, videtur hinc quique
e
aliquid duci posse ad methodu tamentia invertam sit y  b X + g  dX etc. AB1)a BPt7
 vdXe B. H du ero dy p 1b_t ECX + 3d X etc. 
Tot et  7 bex et. Ego XtB  bx + Cx + d X eM (H y
et
 ab +2CXA3d
Quontuocum: in qua: BP sit a X abenus + ex hoc arto, diordat ut et Dy.
set  hac seu VH bX F CxV ou
duidamus per 8. fer. Agy H eB at idem BPF a 
ergo d a X dyr, et Ic seu Y p a- x
dividatur per a  habebitur series infinita aqualis priorii in qua valires e quadrnt ducitur
in valerem dus quadratum posito finiatur alicubi, hubebuntur ae et aquationis instituendae causa, ut
ossit manere x. comparentur terumini terminis, ita litert b. c. d’et. invenientur quod
didetud methodus Hundeni admac brevior sussane, ut fengentemtnvel perpendicularem feccile sine
illa una incognitatantum ivemiendum, cum flusiana elinquat duas: sit:
ri t  A. BB X.  F A pD.  4Bg A.
 B1 B+ 
B. CH S V H x A. euit y ABG AC p, Aet 18  22
0
Hticdralor ipsius y substituendus ubiue in aequatione data. determinand ad duas
adices aequales ut inveniantur A. et D. Hoc in omnibus scaedit d coimis est
qpulum infinitis t pu  9. 3B bx E CX + d er seubetur. A AX+ ex + dX erc
Eoe et piba et  de ex. se i sifeni sculi st ap stebuta isisius trotuafio
Hinc generalis calculus pro invenienda diterentiaa
a + b x + cx + d X et  A+ A X
e
nava
ande frei.
quaerebatur
rs
f + 9X + hx F l X3n O
9. - h1.
fiet 
1-x
 4b. 1 + cX 3+ d
at
3.
2b1.
1g +2 t X + 9 CX
e t  e
hiei Ar fei D decanint sit signumD et  vellim. sit sine
seu et habebimus:  d se
D Ox 1
D p eAt 1 0
Ounde patet quo modo sier
regressum invenionda  ex data:
e
0
 a 1 
0
Ax
B
aut exacte, aut quando in rationaliter
fieri non potest, per seriem infinitam appopiquantemd quantumliber
aequationes notabiles: b  a + b X + CX + d X3 erc. p determinata ad duas radices aequales dat.
b + 2CX + 3dX etc. D Ducatuo hoc in illud fiet D D. Ajo SD n ides (D+D r Z
a
2
itaque a + b X + CX + d X3 er
a + b x + Cx + dX3 cu 2
per b 4 b + 2CX + 3dX vere S  per a + bx + ex L dX3 etS
prorsus ut RX in 1+ 2 +3 4 4 4 5 + 6 etc Y 2
a+ bX+ CX + d∞
Eodem modo suto tesse  a + bX + Cx + dXB ek in b 4 3CX + 6 X2 + 10X 15
Eadem res videtur
imo ista diligentius excutienda. Est hoc determinatio ad tres adices aequales.
redire debere, si b + 2CX  3d X etc. ruisus multiplicetur per 0. 1 2. 3. 4 etc. fiet 2C + 6dX + n etc.
hocum dimidium sat numeros hiangulares: ic +3d X +6.. ecc. videndum quomodo ad possit conciliari
cum directa pultiplicatione per 0. 1 3 6. qua initio multiplicari potest: a + bx + CX eri
videndum et si radices non
inminum video mltiplicando plura ex his satis mira duci possunt.
sint aequales, sed differentiam hhabeant certam, quid fiat. Item nreciproce quallesnam sint illae
aequationes, quae tuto possint ad quod determinentur se multiplicatae ordine per numeros quadratos,
debeant imandere nihilo aequales. aliaque id genus quae quaeri possunt infinita
b( + c() rdd- 1A( o
B
b- A
1