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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 64r, page id 00068049:0127
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via pro diresenteis per radics formularum
in A sit  = S, Xtay X+b :9, X+ C, X+C. sit X -gV+ l, :+n et per
t
DC FB X+ a = gv + hV 1 am: YEm. = at. Y uneu:, hV + m azoribus=
Et. er ubi si duo ex lis possent aequari
ph. cmts gV + C
et y= Seit Y + anc ib anY B, V + 1
pes esset in vado. vn  sed video rem non esse possiblem ponamque essem
24+ qch = g + atr seu
et q + qc m = l’+am
T+ ah V + l’Fani 9, g+ch Y + V + im. sit
g2 9+ ah: stch,  l+ am: (+Cm
41
fiet: 1)  + abB+ cgm H achm = (91+ chi + agtr + Cac tm) fietque
9: h = l: mm. ed ita X
procurare liael expari causa
e
L1
 G:h = A C- aH: c= a Mm unde seu
ntra interende nec ex traribilitatem
Eadem methodo altiqus: X = 11 B + RV + 13, 20v + 21V + 22. fietque
sit jam:
 + 1
2: 20V + 21V +2
non est constans.
1 - 20 a VV L (2- 21 a V + (3 - 224 = 9, 11 - 20b∞V + 12, 2IbV + 13 - 216
177
+1 YV L
X +a = -20a
fiet  q 1 - 20 api, 11 - 20b = 12 - 21 a, : 12 - 21 b, = 13 - 22a, : 13-22b
61
seu (11. 12) = 1. 21B = 12. 20+ (10. 71 aB = (11. 12) - 11. 21 a = 12, 20b. f 20. 21. ab)
et fit 11. 2C =. 11. 21 a - b  12. 20 a - b, seu 11. 21 = 12. 20 et pari jure
exoqe. 17. sitet 1 2 = seu 11. 20 = 12: 21 et pari jure ex eq er fiet
et pari juve ex aeq. 17 fiet 13. 22 = 12: 21 quibus substitutis in 
valore capius XC X aeqliore 2. set X HV.
fB 1220: 21 VB + 12V + 12. 22: 21,: 20vv + 21V + 22
tinc sed pari junc etiam fiet concidet reb. quus factae numeraloris
cum relisfactoren aequabuntur duo factoret nonnaloris
c
Xe
ans factor nomnaldeis alteri in artitariam Y, (ol supra
ducta aquantur et fet p seu X 12nO∞B+ 12. 21V + 12. 22
20. 21 YV + 21, 21V + 21 22
sed in fie X  12 et e ex 1Y 16 931 12 - 21a;, 12- 2b
21
et quia eodem modo connesa sponte sua ex positis ob parita
tem juris instar equationit 14 aequattur facto res. nomu.
16 raloris unus per alium diorsus relinquit Y loco g. ita ut
fiet
x = 12. 20VP + 12. 21 P+ 12. 2 =
20. 21W + 2. 2VF 2. 22 2
sit Y = 12 - 21C,: 12-21C. Itaque caeteris omnbus existentions
et et
ubi tano 12
extahicilibus santum q:Y aequatus est sub radice
fit g: Y = S12 - 21a, 12 - 218: 12 - 21b, 12 -2)C
et 21 = 40v + 41 e
20
(27)
quam 21. explicanto per V, ficret 12 = 31V + 32
122 -2. 21 a + 21. 21 aC = et 43, V + 2. 31. 32 V + 32. 32
ta 40V+ 40. 41 V + 11. 41ac
are 31. +0 - ate 31. 41 V - are 32. 41
12 - 21a, 1-2IC
au
et, si volumue tollere YD fec 31.31. + +  aC - a Fr. 31. 40 20
sed pulo tiustra in haec in quiri cum explicatio ipsius 12 et 21 per V scunde
BC. 40V
et sim part 31. 31 + 40 aC - R+ C. 31. 40 =0
Non ergo aportet adhibere aeq. 1f et aequare
integros factores quadalicos, sed tantum redtere 20r condirisibiles, parique jure in
uit possit dare novi
nominatore, et facere demunc unum tactorem, numeratoris condivisibilem uni fa-
alis
vide cmus Ergo an is- 204 vV
+ 1 -21a V = 13- 224 et p - 2cb v∞ + 12 = 21b V + 13 - 22b sit condivisibiles, per compendium
rori nominatoris. Et ita haberetur venressio.
si  30∞V +31 V + 3E5 condivisib, cum 400v + 41V +42 sit SC 13042 +39. 31.45 - 30. 31. 41. 42
C
0
31. 31. 40. 41
AV. 46 31. 40. 42 bis 30.92. 4042
sitatis alibi inventa, vel etiam  32. 30. 4 - 31. 402-3150. 41 - 31 40, 30. 92 3L40103 n X)
n ubi si unum gotum ingrdientium comprehensivorum sit 20. erit et alteruu tentemus unum sit
per theoremata condioisib
31 =(- 20a. (Z - 21 b = 1 = 20b. 12 - 21a = 11. 12 = 11. 21 b - +2. 20 + 20.2 ab - 11. 12 + 11. 21 a f 12. 20b - 20. 21 ab -
= 11. 21 - 12. 20. a - b = 30. 41 = 21. 40 et 30. 42- 32. 40 = 11 = 20a5 13 - 29b, 1 = 206. 13- 32a = 11. (2- 1122b
Loa + 20. 22ab - 1. 13 4 11. 22. a + 13, 20b = 20. 21 ab = 11. 22 - 13. 20. a - b. Ergo hac cx54. 17 diusa per a b
het O = 13- 22a, f111. 21 - 12. 20 4 17 - 21a . 11. 2] - 12. 20. 15. 22. p 13. 20 f 1- 20a F(11. 22- 13. 2
substicuamus c et A in ag. c∞ et in non fnatore Herent esset condivisibilitas, renique
similiter si pro a et b
si in aeq. 18 pro a et b substi.
habebitur qdivisibilitas in numeratore et nominat re adeo hic
ubstituamus a C  a et E simul concurrent
aes
u e souma