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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 219v, page id 00068196:0434
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Sit uine formula
70tratpxxtek,
pX + n. + etc. 6. et. volumus no
tollere terminus summum et  secupdum fiat X = GC 1902191, a : 80ZF∞1, et fiet
+10,  + e 101Z t et
+ H. 100. 200 N. 100. 201 do q. t ek
+12108 300. 4
10. 100   GC l+ 10. P. 1011.7
11. 100:3. 200
 l
12100200. d 1
13. 103 0 d4
+M. Crtooal ..
+, 11. 100214.0..
1. H 72 V.4, 
FB3. C3 aa21..
+3.13. 103 200,20)4.
sageni
rCC 200220)
s
+12. B1204 . 
+2. 12. 1. 500301 -.
ei odi titor Z
1. 104. 2. Z 711
20027+ 2 200. 201Z
ubi primum terminum faciendo aequa
tem crihilo habetur ratio inte–
100 et 200, seu 100: 200, per
aequationem quae origetur si fommul
proposita esset aequitio
lenm nihilo habetur ratio inter
VoB at, 20), seu  101: 201
2 200Z + 201 5. _ hic si velleus valtere utrum
terminum fieret 200: 100 = = 19: 11 = 201: 101. sed hor mplicet, nam ita X
ita num ita sip X fieret constans sante Z + (101: 100) =  seu Z- 10a: 11 = 0
sed verum quia ita 8 ipsiu 2 priore modo fieret x - a, quod non licet
posteriore vero nullus haberetur. Vator ipsius X, adeoque nec ejus explicatio
tollerse non
aut formulae mutatio Ergo novissime absolutam mutare
non licef
videamus an in aformula secundis gradus ut XdioXxFHX+ 12 liceat
tom tollere simul terminum primam et secundum faciendo ut prius x: 4- 002+
fiet 410. 100 10047Z + 2. 10. 1001017, = 10. 101. 101a  Ni c sulalotermino primo, fiet
i. Nu Y1(., 100. 200477+ A Daa 101 aZ +, 11. 101. 20) a  i o 18. 100 4 A. 11100. 200 + 12200. 200 = 0
d + gHL (O1. 2004Z ecp  in Sin 1010. 100100 aq + 10100 a. 1. 200 + -1. 1. 200. 200
memr _ 12. 29. ∞Z F 2. 12. 200. 201. Z Fe12. 201. 201
X= L 11. 11,200. 200= 12, 200.200
 seu 10. 100. 4 = 1. 200 =  200)(4 11. 11 - 12)
100 (Fum 2) L  Pari jere D00 1xa
Neu 2002
nam signa hic sunt opposita  irrationalium
ambignitate. attautem recundus, etiam terminus destuatur, siet
adat
seu 201 524aa + . NVa (a Y IL.I = 10. 12) - = 117 : 12)
10p bu
10
12
e frara nL. 1919
 01 = - 2. 10. 100a a   I1. 260a
n 2
2. 12. 206  11. 100 a
seu 20t L
 1. Ha, 4 2. 12(_s( (1- 10. 12)  L 11 . 11Z
2. 10. 121 = 1. 5 . 11  u1.
na en a YC u 10. 12)H 110)
mttr t un
 ne
et pla
at e00 (t. AVC LH1iore) L Ht d 
duo tergu sumri sunt oltendi non minus brevis est
t
100 F re
et maris est tum st generalitatem tum s quia ita netomentis calculi
Interim via per radice forimuli cungia
opus nom est praeferenda videtur
ab Esto formulae trium geauum ru
ees xX facta ex AL D,X41, et a fat X- 90Z+ 9B, F 8Z+ 81.,
formula erit productum ex +902. F 91a
t f.81
 qu aZ + ha  aZ t _ta
31. et
 41. 81
ubi falieuus 90: 80= - 1: a quotcunque sunt agradus. ptollendo Terio samino seu primo
sed proi gollendo deimino secundo cunique gradus sult duous sator terminum primum esse
desinctum, utique pat secundo destrendo solum opus sit hacunna bicrivne
aZ + 31. 8C,91 a +71-81 = e Sed inde video oriri absurdum nam hinc necessee
vel 90 aZ + 31. 80 0 sed sa oporloret esse 31 = 21, id est forent duae radices aequales
vel onvite et fucchre gla +24. 84 = 0. sed ita fieret Ali 81 = 90: 8 quod etiam non licet
ita jublatio ut duorum summorum terminctum in aeq. quadlatica non procedit. Sed bene
summi saeciendo. 9ea +21.80 =0 et 91 a f31. 81 =0, in tertio gradu pro sublatione
secundi termini primi termini, manentr qua t 180- 0 tioha ternions e0 sint quiim mat
moductum ex l90a F31. 80, 90a + 4140, 91a +21. 81 = 0 ld non li A (acre 91 a + 481=4 alioqui fieret
91: 81- 190: 80 sit 
retur, 8. 5d sed ne licet facere, qua + 31 40 20 vut qua +. 4180 = 0, alisqui ge novei
retur g0: d t aus  has  ut decaectio in sutari
Endo rqua vel xxtete
Applicemus ad formutam simplicissimam situe formula talis 10X +.11 facientoque
10X L H X = 100Z + 101,:, 200Z + 201, fiet
+41. 200Z + 11. 201
ida
aoem
Ergo initio hujus plagulae
imos termitios