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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 389v, page id 00068196:0774
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mo) X =
Gpehpy Aipp yr4. vat (Edu) srm =
+92 y+s, y+W
Aequationes assumtae et praestandae
(mo) X-
dyyarabyraC, via
3rb, p, ytq ver, yts
Aequatio ex 1. deducta,  (4to) X+m =
debet esse (O ∞ D
ayripcyrece
ay + 2acyy+ acc y
r ap.. + racp. + aecp
cenence
m
y+4
31b, ytr, y+ 8
et ex aeq. 2. fit similiter Cto) Xtm= egytresyt ess. yrp, 325
(6t0)
ay+ 2acy3 + accy
ap.. raep  racep.
ag. +racq. + accg.
apq. tagpu. + accpq
non, (, p. 2) mi + 2mb yt + mbb yy
mr. ambr. mobrus
ms.  Embs. mbbs..
Mrs. Embrs.. mbbrs
Eodem modo
(imd) e= a + m
3+b, y+ Y, y+5
SQ  et fiet 6 ex C pro m ponendo n
F
D ex Q pro se  e, foB, Y Ib etc sunt communes ett ( l commuris
ponendo R, 9,95
itaque aequationes identificatrices jam instituomus.
(2do) h = a+n itaque e, et h, haberi possunt pro datis
3ti) pS racF an+ aq = (2 ef + ept es -( per 1) 2a 5 + 2mf + apmp + a S m 5)
fit mr n (4t) a5 - mp = + 2ac, +aq
curi jure
11. 1I1. 110. 101, 100, 3H.510. frl.500
+
multiplicetur aeq. 4 per n, et ns et aeqis per a, et producndaddantur invicem,
simstra simistrae et dextra dextrae, fiet ibto) aat- mnBn = ranc + 2mub-rans 2mnstanq- mnp
raa c + 2anb = 2aag- 2ang t aap = anq
et pari jure multiplicetur aeq. 5 per M, et aeq4 per a, et productae addantur invicem, sinistra
simistiae, dexta dextrae fiet ua-mn 5 = +2ame + mnb -2amg - 2 mng  amp- minq tubemus ergo r et S
42aac +ramb- 2a a t-ramf + aaq am
Hactenus coincidentiavimus terminos primum et secundum, quaera idem quaerendo r et s
nunc rursus coincidentiemus ultimum et penultimum, quaeriendo p.et g, subsditutis pro
quod unt fiat commodius, et ne calculis prolixioribus involvamur, aequa
tiones 6 et 7 tam compendiose exprimemus, ut solum appareant, ri s, p, q quibus et ex aeg.  fiat
r et svaloribus inventis:
et  naito + p e s traito +9
dlotaxilo Xu. nagnoi
Ex termino ultimo estu eff ps = a acepg + mbbrs seu per 1, est afsps + nHps.  semque
modo ex aeg. 7 fiet _ (omo) 104 s-q = 12 ap
pari jure fit (2mo) hgggr = accpq + nbbrS unde (3() fit efs ps - hg9 qY =  m -n bbrs
sed hac q. non est opus. Bllamus s, et ex e2 fiet est ps = acepgs + mbbsnaito a mbbsp
Ay agq n et 12 tollamus Y et S, f et ex 11 fidt efspus + efs p12a 10 = acepq. + mbbpus + n bb pagnrap, mb11. 12aa
(15)
et ex 12 Galo) hggDG + RBgraO = a ccpq + n bopq + ebb naptaq + m bb. H2 aa
n rahc +2 enb - 2enf - rahg, iaa copendro A. 4 1010 f +10019 + 1000 a  1a 10.c
ubi 10 est data nam 10 = aa- mn, : a
Follamus etiam ret s ex terminis penustimo  hacc + numbi Amg -raeso
et fret
ext penultime q
i
as accsue a amque rrachus + mbbB t mbtetasio t orttus t tlreus ubpus +peb aq Lmtnaro pae en buagrnax F rmbuinaa  esse t e es + esfu te nanores p trespnaio
et medio
anc acq ta tracpus + mblsque + nbbserazio tnlbo tntbram + ub pu ee
C C  motaxinaque + unb muna (L hoyot E  tggP + hgg 1a 10 tahg p9 + etge qua . 10
 du tagi amqu tape umdb. anties siud ittuea tu pyt B engterae nunaa e etst resue t resium rex eap ue )in li d  es qntimibs sognit ut cont 
+obb trat uatua +an sasta) An nous  nogt atique tangnario + paquio 5
Assemus jam ope aqu. 20 et 2I invenire p et q. et earum ope tollere has literas ex aeggs. 13. 14, 18, 19, Sed idem tamen faciemus pouto compendiosius, si prius
ita ex 13 et 14 v nastetur 59. 2t sine pus, et ex 18 et 19 nascetur aeq. 23 sine
t, tollendo B3 a  14, itemque 18 a 19. haber
Ai ac +eI
tollams itiiem, 0g ex 18 et 14 conjunatis, et  atidem ex 18, et 19 conjunctis
quo
quae aequ
pro cegq. 13, et, 18, (9 rese Betive suibumus. 1MBF et soq o  2 rup rrioap Copaatrova Ld, At 3upg + Sroup + Joaq r ovao et An pus E urapeo aytaa
et
ebit
Envetia fil e) on noru s tioma  oaita  Et exIi sil BIoGnA F oN AUAq + 300. du pa So copendio rp
compentio  sp + a (p + (0 9 + (100) a = o et (2,10 +o +2 oda -unde seu 4 113L201 p L (101)20) 4+ 400lepia C = 0. et
Yo1. 311
et prr his fubsti t. Eado valores fit 410. 217(301. 411
10. Mi St ro1. Sii lp
1100. 21125301. 4119
2 100. 111S2 ac1. 31 fa
∞5101. 211(300. 411
(+)
0
21D PC 1101) 219- 10eosa
in aEp+ta
t
5. 211(310L4 11)
5
ithaco uta=
a, m, n dats
hwy teligyshigae, 32
xin-
extassi oepu
Eto
260) tam
ytp
+b 1
agypracynace, 9. p, ytq +myytumbyyem bb, vi y1d = C
12. 2. 20 201. 300 4 11. 410.
(25
3
ep.
 2055.
+ efsp
5.
ep s.. 2 es p.. + ets p.
1821115300. 4 11
l201. 1115400. 211
=1 101. 2IIY31O.HI (I
pis
9. 1II.41D. Si)
aetimumi erit hos vaotes p et p substitui in a49. t8+ 19 13. 14, 18, 10
episa d se