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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 5
# Folio 14r, page id 00068002:0027
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Tun theorema generle
potestatis Polynomiil affecti
redit ad potestatem Rino mii
affecti, nam
et
P- 1
2 qe2 52
perseries infinitas, aliaque pluroma huus generis jam a me alisque
reperta et partim edita, nullo negotio exvent exhibentur derivantur
possunt vel ex hoc solo Theoremate extractionis Badicis
Quadraticae per seriem infinitam nullo negotio inveniri dimensiones ari
recipiunt quantitates jam inventae membrum ingredientes. Exempli circuli, Ellipseos, Hyperbolae, et arcuum quoque, per seriem scilicet
infinitam. sit exim exempli causa Diameter circuli 1, sinus
Versus X Circuli radius _1 sinus complementi. X
erit y = a x) ( X
e fit
et 1- et 13vel. 4 del 2 etc =9
inus recs
fiet 20 = 1 et 21 =0 et 2 et 23 =0 et 24 = -
et 25 = 0 et 26 = d. 3= et 27 = 0 et 28 = - 1. 3. 5
83 1. 2.3
adeo tandem erit Ae y = ((I- XX)
- 1-
g-7 - 1+ + X
4, 1. 2
1-
1. 3
1671. 2.3. 4
= 8, 1. 2. 3
4, 1. 2
16( 1.3,5 28 1.3. 5. 7
X13 X
16, 1. 234
1. 3.5 -7
32, 1. 03.45
3 = 1.3,5. 7
32, 1.23.4.51
1.3. 5. 7.
et Syax = X- 2 13 X. B
64, 1. 23, 1. 5.01
Xt.
quae est area zonae inter radium et esthum rectum, arcumque et sinum complementi v
A, 1. 2,3
8 l.2. 3 etum ei 16, 123.4,9
comprehensae; posito 1 esse radium, et x sinum compler as ve
quae est area zonae circularis conp cujus la inter quam ductus radio
Barallelus sinus complementi cum simu re abscindit, quaeque adei praeter
Fradium et sicum complementi etiam sim rect et arcu continetur
sed arcus ipse erit
x + 1- X + 1. 3
231,3.
X + 1. 3.5 X
A, 1. 2,5
8, 1. 23, 7
1.3.5. 7.
X etC
16, 1.23.4, 9
potyaomii,
E. Eadem haberentur ex Theoremate Generati (ad
ct Nam quoniam e hic non nisi de Binomio
agitur. nim (e) a+ b) generalitem = e +
cauonem deneralim Polynomiia affecti
exaneralitet
Operae pretium etiam est Teorema)
contrahere ad Fheoreum generalem polynomii simplicis; ponendo X= 1
canonem
X = 1 et pro 10, H, 12, B3, etc. resumendo a, b, 1dC, d etc
quoniam nulle amplius indicandae sunt quantitatum potentiae virtuales
relatae ad X. Sed tunc pro et p pls membro in Theoremate
palnonni affecti posi perinde ac si fuisset y =  10 + 11 + 12 +B et
sed ita pro membro simplice potusnomis affecti Canonis polynomi: effecti
ema
affecti, ponendis est eanon ponenda est forma integra potumani in Canone
Polynomii simplicis, quoniam enim x abest, non ampluus divelli necesse
in
est a se invicem membra ejusdemformae Exempli ausa
canone polynoraii affecti non possunt in unum conjungi 10c- 12 et 10
et  1 12. quoniam gradus illiu et quoniam pritiss habet cum X tut primum dat
sreptu
10t 12 X secundum 10 13X, tertium 11 12 _X, quod in de Canone
polynomii affecti non occurtit nisi latenter; nisi malimus adjicere illi jam tum
eas formulas quas in casu 10, vel 10, _ et u, et 10 et I1 et 12
simul evanescentium substituendas tantum praescripsimus, quod
utique sano sensu permissum esst. Sed in Canone polynomii simplicis
statim possunt deben conjungi membra omnia, ut adeo quodammodo
in speciem  magis sit compositus (anone simplics pol affecti
sed operae preti pretium erit utrunoque Canont exhibere initic,
utriusque
come
saltem ut collatio melius appare C
comparare inter se
aspectui subjiciendo
10
12
2 =8 ergo n = 4
e recum nniones
ente
1.3.5.
16, 1 2. 3. 4
cF -
: GV
CF. BL= CB. Ep
de edu 0
dy= = Exdx
X Si XX
dxe faxidus =
si ut
FB-
Ge