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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 66r, page id 00068255:0131
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Ad Ex articuli 1g aequo 27 fit per aequ. 25
+(12518 123 126i 5
7123
sis errin
sas
23712
+M (237120
(12543 (23612, 1723. 12529. 23512 4 1712. 23512011723
R712
cplalis n lems tots
+23on brr) 1971 F
nnesuoq - 7u2 (2 5 23) 23113)
+, (272 (137125) = 1723 23512. 12723 - 1712. 12 523. 23712
(12523. 23712)
His ita correctis Numerator utinque solo differunt signo. Ergo cum natsferendo mulando
(12523. 23714)
seu fit namfil = 7123. 12523. 14723 + 7112. 23512. 27712 (28) = 7123. 12513. 12723  - 7112. 23512. 23712
saequ.
in A (D 17Z. 1 523. 23712 4 1712. 23512. 1272)
+1723. 23512. 12723 - 7112. 72513, 23712
itaque mutatis signis alterutrius aequantur denominatores, fietque
112. 12513. 23712 4. 1723. 42512. 12723 = + 1712,23512. 12723 F1723. 12523, 23712
sel Atq adio tandem  seu 1H2B,  125 23. 2372 + 23512. 12723 aequ. p 23~12523. 23712 + 23512. 12723
aut denique  e 1712 = 1723, 12523. 23712 + 23512. 12723=0. unde ( vel erit 1712 = 1723
ispi
Eodem modo ut ex aeqque. y et 13 articuli B duximus aequationes
(progressus
ipterin sic ht donce quid praestet ostendat
et 4’articuli 19. ad eoque et equ. 23.24 ejusdem
14 et aequ  art
articuli 19, ita possimus et  consequentias instituere ex aeq. 12 et 14 apticuli 18. conferendo cum adiil  lsian. , iorii
ait Nempe  aequ. 1. articuli 18 conjuncta cum aequ. 12 artici dabil fretque 1723. A. 7_ - 1712523. X2,:
15 nempe fit 512 = - (15: 1) 23512: 123 et
17. 4) 28712: 327 et723 f(97: a) 12 3: 3M quibus substitutiis in aequ. 30 fiet
:, 12. 133, 12523 + 23S12. Tollamus jam 12.3723, 312, g3. per 10g9. 8. 10 articali s 4 et aequs 1 l. 2. au
et 523 =  (15: a) 12523: 112
1722 (15: a). 238(2. 131. e) 13
 1712. (5: a) 12523 (57, a) 23712. . 312 (15) 12523, 23512, 12523 - ∞512
15d =
(112. 1239, 12523 + 23512
- 1723. 23(12. 17 252. 12. 113 + 1712. 125251 23712. 1 312:, 7HB. 27115. 19. 312 4 712. 12725. 12. 323 = 12523. 23312, 12 523, 23 SI, :, 125137 2512
e
(31)
+7 23. 128. 63 
alterntra per + muliplitato
permulat
+7u2. 128)X, 
s + erch. 23515. 12725. 1 2. 323,:, -7123 1  qu as  ish. 1 . s. nd s
ationem
c. 15 data
A(413 ∞12. 12
ol. 5 cum d et 7, inde 71 mutant signa
ue rerliced aqu fiet
3, Hsu3. 1911
sSS. An rS Aum nchtsIG= ( 23.33 512) 25ig - 13513: nsuB+.
atae dat - 1713. 22512. 12723 F 1 7C 12 523. 23712,:, 4 713. 4 23512. 23712 + H12. 12513 p273 = (3tio ) 12523 - 13512,:, 12523+ 13 5 12. Et parisare permotundo
 pari jure
fietue - 173. 12845 29)
interse latera
18 conju
lis 33,24, articuli 19 Et pr
3 123. 312 p
umus exa
13. X35 12. 2572 - 713. 12513. pr2g -B 4to 1927 23, 20712. 1213 t enia  ivilio 
iistrosum denominato res non differunt in
signis. Erso n
eligimssiriorem aequationem
12238.
2tsi2. 27E3 = 171L. 13 23. 2372 = 41727 12523. 12712 A 1712. 3 
Unde erit vel 1723 = B, 112 vel 12523, 23712)=-
et fil 172
SI2. 1272
d aequiq cum dictis huc
quepur
endo si cons 3 et 32, quod frisset optimur
uantur
us suneratores
ce grmus daq.29
+ 66t0)   te a  3 ad 33
3o
oex 6. f. 24
fiet: - 1723. 12527 23 112 + l12 233
+g. 123252(3512. 12723 + 712. 2331E(1523 2372 , l, 1723. 12523. 23712 = 1712. 23512. 1272L (12513) 63 ∞12 125
Si ae49.
fit L7123. 12923. 12723-712
oportecisset incipere et.
arius
ase 194. 31 ,82, 36, 37 fui
ut aequatae Aequabimus jati
l. Jam vel 34 et 3
omnibs per by12.5323a fiet
112. 5y2 4
tu
1323Faa  (5328- aa
v 1712. 1723 = aa seu 1712, 172) = 1. fietti. 12+
progressus doc
123+523, 1g 323+723
r. 115
512 et 523
235123:3 12523423512. lir
, 112. 123a + 15, 12523, 31. 323a-37, 237
112. 12
te  et 17, quae to dant idem. qui oilere aequalio
23a +37. 12
10) 112+512,:, 312 +712 = (112. 123a - 1
os duos natore
nendo sit +eras    E
EL
(2)X112. 1923 4. 711
jam  123 - 713 fieret
intati
et multiplicatis
di oii ate i iies t tres dide
5325 t suhaata
sitaa
ligonum
eodem icto
 ee pr
aten multiplicato per + fiat  L. 1725. 235 P. 12r25 + n. neriar
 (2) 1712. 1723 = 4 7123 duHes
7H12. 712320
512313at
ne tractare aequationes,
. 12527. 235I2. 17223IE L 12. 112323,3 2772 + 1122,7112. 12523. 12725 - 7112. 12523. 3512. 12723. 237 12.
dividi possant omnia per torum quudratum, et fieret = 1723 (1712
Erro fiet 17i2i
= 42 st 13
a
ny seh
S2-fy23. si
int itrois qrtira
ai ttores per atdiu
 siia
13712).
i12. 123,:, 312. 323. quod f et secundum, in stothes (t) a sed
in video alter
eore pednolonam er pncei 
aequari alter
vel 3t tuileq. 3.
piset e
49. 2, 24, 36,37
el 34 et 36. sed prius pla  5 +
+723 vel ouendio 522 +
potam
93+523= 112. 17) a + nes 15. 13
. 323 a + 37. 12725)112: 312
7. 12723,: 312 Hinc C
p2. 123a + 1512513,:)
ii (4) sit - fiet 5712. ∞2
Sir, ayt si ) t eyemo
iutem praestet, rectaagulumque an fa ara - 5. 2351
sit 42+ st2 (2d0)) 112 + 512
et 323 +723a-
i
25sZ + siaa el sye cr a-  sintrs s
d Possent ad hus saquari  
nem quae determinavit esse
et fit 5312. 5723
312. 323at
at
Exaq
71
1)723. 1712. 23512. 1523. 12725, 2371
2351211
12523. 23712
Seu Malialiando per + et trauspe
sid. ag. 7. per ag. 7
nnoliiltto
ex artiaiti ib iqu ue 13 dupinus aqu. a 23
piticuli a5
alteutae aotem putter volclisemus tractare
deinde ixi