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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 82v, page id 00068049:0164
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e
simplices
CIdeamus quasuam fonmulas irrationales reducere liceat
a formutam irrationalem duplicem  seu implicatam, sive
ut vulgo vocant Ueniversalem 21. Hoc ita fiet in exemplo
CH
X + bXY CX, +EX +f d-X soxtf-et
 = X + 2CX + 2f)
et fiet 
+ coca ux + 2 fCOX +
+2O XX + Xf X + 2fC0 =O
 coco
Xa bX + C =  h+  X = e
sit formula X x + 12X + 124 V 14,
aequanda quadrabus 132 h +2. 132. 133 h + 133 : h, tunc actu extra hendo fiet
e
23)
+ 132t + 2. 132. 133h + 132
e 80124 hi
+2 128 hh
ec
1
Cipsi
Quae formula per omnia similis est aequabioni 21 (adeoque et 20
modo faciamus numerum assumtitium 101 (adeoque et 55,
aequalem nihilo
Valde memrabilis videtur via initio hujus paginae, quia ita differentia in summnado comptehensi
et explicanda nil turbat, verb. gr: A iogu ngx gy + ayx + bXX + y + eb+ f
noguept assumta sumatur valor X = m∞ + n: v+ P, quo substituto in aeq. 1. siet
LVIt 2pH+ pB yy + ay. v+ p. motn +, m. ∞ + 2 mav +nn = (4 vD + EpoF
 e mv+n v+p + f v + 2pB + pp. = 0 Haec aequatio coparari pt datae
ad lineam propositam, nam reduci potest ad quadratura avalem quod
sic estendo: aequ. 3. sit data, ergo inea  figurae quam expriunt
quadratura datur si detur. ydv. pajam pro V substituas y, ut
hubet aeq. 2. habebsis aeq. 1. in qua datur  per extractionem tuusferma
tionis in rationate capatem, explicardos B rationaliter per 2. et
N dv etiam datur ruvaliter ex x differentiando aequadem _. Ergo
l
ta
est ad ravalem
tota quadraturque qua sita  o
valde memorabitis videtur via
Ex aeg. 3 fiet. fs n m  2 mn _ P n n_ (4) am B + anq  gy) initio hujus paginae quiagita differen
mp
n
anp
=2p5
due
+C V + CP
∞ + P
i in sypengndo caprehensa, non
Ambat. siter+ ex+ ec assu
X + gquo LX t om
qeu
+v, 7
Aex + ex + de etooxis
procu figum quartanda, itaque quaeritu
valore
Cydx. Ergo pro v sulistituent
y) et habebitur s hatimaliter per;
et N0 exaeg. 2 habebitur iraliogarita
sed reotitici
porae aquadis
padratura
E
229
3
sut
u
ras
hac
tam
rancs
= n
Epsi
pr
tramnis + a
Aramep
42 an C
(2CC
+ ranc
+ cepp
a ∞92
etfinemm 
2sa
tcc
.Ter volatur X hadibiureus 3.in
sumatur v Bex
 punturfint g.
smatu
amni
y assurger ad   yy, et v ad vE. quae cri
2+ M. Ex
amvan
- c - ep
 ad aeg. 3 ∞g. 2. fiet aeg. 1.
p
B ZV + 2P Intrinallum reducta est. Tpatama XX = bg - CX- eC, substituatur in 5q, 2. fit 1V= By. Gex.
ventis ad rationalitatem. Ergo quadratota aegu
d
sn XE +by- SeE +99- veo: scat, quos Rursus in vy. 1 et 2. mulliplicando per aucem
fit gg ee  sit sgbus - 39XX  oex  e vD sit , eC- by 99. vv Z =XXG9 +XX VB-exg ot  BV
et u 9. per 10 fiet
-2XXeC F +XXby - fxeC + f_bq et dibisis omnibus per x fiet: X
X = C99- v - feC + fby,: 5ee - sby eq-49 + bB, adeoque fiet ex 3 et 8 f19)
Sec gg -5cevr - Sefee - 5cfby - f cgg+ ferv + ff eeffby(+ 6)2) 4by - 5 ee t 9g - 00h=
et sC-  vocesdi n et ex aqut put b
6 sndu causa Aet Lg voceti th
et ex aq. 8. fin ( M3 - cv∞ + fby,:, D-bu - tih + vV. Ergo denique aequando 12 et 14, sietsm n3 - mC vV + m f by 4   bYVB 1t. h v V G lH+ Ggit
compendii causa sit mn + h
mC + ath = gq C. nf b + Slabla hu5 b +2. Gfh = Y3. Ergo ex 15 per 15. 17. 18, fit pF - q v0 + v+ + Y)  35. brBy +5 5+by9L
compendio -10 = 18y + 12gy2. f. - 10
Y
4. 5br vu+ 4. 5 5BV
seu y = Y. 25t 15bq 1b  4556 V
2= y1: 12 + ye seu P ∞50 12 + 1183: 412 = 11: 4. V 4 y 113: 12 + yy5 C1= 410 - n
= r3 =+ 2. 5 bb vB, : 2. 12 qi
eu
vanuit in vinento est qua
tae
ponem
inem connesbentila
potuisset contingnes si in aeq. 1. scripsisemus by = XX L Cx +XX+
terminis, ut p 4
Id sib elatere ponita
sd
2.1
tura et
CX +CC
poaiturs, u sensi loco e ponatur Ct 17, quruum in fie pudem seceri sinus
nam ita Deudesi ac si
16Hrg 32 Be+ i