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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 6v, page id 00068196:0012
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Adeoque 112. 323 = 123. 312) Et 70or = vop. 3 1
Habemus ergo 32 = 112. 113: 313 323 =123. 113.313 300r e 10opr 319 n (223 = 123. 112:21
unde 100p = 2009. 713: 3. Adeoque 300r = 2009. 213. 313: 113, 13
Sed dubito tamen an ob aequationem 15 commode facereliceat  uZ. 1 3 22. 223=9
ita enim ex ea fiet po= 2009. 213: 113, Ergo fieret 212 = 213, nisi forte in calculo pecca
vis postrema Hypothesis a dat suam consequentiam ex aequa5, ibi enim ts fiat
112. 123-212. 223=0 fit etiam I13. (0p = 213. 2009. Sed videamus arares
an non aliquid subsit incommodi. 21  32 32) fiet X2. 223 = u2 113. 113. 123. 313. 313
seu 212. 223. 313. 313 - 112. 123.813 113,: 313. 313, ubi si loco 22Bsubstituamus valorem
123. H2: 212 fiet H2 H2 12 123 313, 313 H2 13, 113. 113: 313. 313, seu fiet
(112 +23: 317. 318) (313. 313 113H3, ubi tamen mhil ta commodi vaded
Si in aeq. D (facta ex divisione aequationis ) matuissemus facere 112. 123. 113. 113= 22
212. 223. 313. 313, prodiret alius valor ipsius 223, nempe 112. 123, 13. 113,: 212. 313. 31, et
foret 100p = 2004. 113. 213: 313.313 et 300r = 2009. 213.313 Qua periade est
ac si locoaequationis 15 ad hibuissemus ag. 16 et ibi fxissemus 212. 23 = 3 12. 323.
id est explicando 312, et 323C, si fecissemns 212. 223= U2. 113.13. 113:313.313, seu H. 1e. 113 3
Oallem Alterutram ergo Hypothesin sequilicet, nec refert, quam eligamus.
Matussem aliquam lecemjustitiae observantem; sed talis non datur  disi impossibilis
quae faceet quae faceret 113. 113 + 313. 313 = 0 sed eo sine necessitate recurrere non
ut jam est factum.
pladet; etsi calculum daret, sed imaginarias adhibentem.
Hypothesui, quod 223 = 123. 112,1.  itaque habemas ut jam dictum:
323 = 123. 113: 313 (adeoque 323:123 = 312: 112) et 300r = 100p. 313: 113
Deinde ob 223=123. 112: 212, fit 100p = 2009. 213: 113 adeoque 300r = 2009. 213 313: 113. 113.
Hinc porro quia per 13 est Z = 112. 100p -212. 2009,:, 213. 223 -113. 123, ideo explicando p et
2(2) = 112. 113. 313.
223, fiet Z = 112. 2009 (213: 113) -212. 201,:, 213.123 (1121212)-113. 123, adeoque erit
y- 1009, H2  112.212. 213 - 113. 212.212,:3131y 213= 12. 113. 123. 213 -112 113, 113. 123
seu Z = 1009 (212 :, 112. 113, 113), 112. 213 -113. 212, :, 213-113. Sed jam ode video mait actum
tam ad 4. alioqui
debent Ze,  a , ZG y, y, Z habere rationem derum est conmpat
nulla est difficultas in extractione
neque enim
damus au recat facere ut e conrssat
+. 313. 31: 31.
2. 12.
13. 713=30= 127
Mquit quoipu e rabetur
adeoque 323: 123 = 312 : 112) st 300r = 100p. 313: 113
2113. 100p:, 212. 223 112. 123. seu per a9. 8
12. 223 - 112. 123 G = 113. 313. 313. 100p.-, 112. 113. 113,. 123 f 112. 313.313. 123 =112. 923. 313.313. adeoque fiet
112. 113:313 et 323= 123. 113.313
212225. 11. 143 fiet Z= 112. 100 p + 212. 2009,: 113. 123 et 
=12. 13 + 315 3 3tidem y = 313. 313. 100p : 112. 113, 123 Ex 49 17 V = 213, 2009 -123. 100p, : 112. 113
223 subistituendo valorem ex aeq. Q fil v = 112. 42 ++13. 42 112 13. 2009 = 113, 100p, : 112. 113. seu fiet
V = 612. 113. 113. 123 + 112. 313.313. 123) 20092123 1313,313,212. 100p, : 112. 113. 313. 313. 212
13. 113+ 313, 313
H3. 11Z + 112. 124
Hideamque an contrahendi causa liceat assumere  313. 31 = 12. 123, fieret 212. 223
pt y = 100p : 113 et V = (113. 113 4 112. 123)2009-123, 212. 100p: 112. 113. 212
sed exsectemus potius duu ad postrema perveniamus, ie arbitrarias consumamus ante tempus.
actenus fatis fecimus aequationibus ductis ex irrationalibus. Aequemus jam rationales quan
+ (123 - 3237) yZ + 100 pb- 206 Y -ab +ad = 0 et explicando 312, 323,
Et primum aequandovalores ex aequ 10 et 2
fiet H12. 12. (313.313- 113 13) C vy + 313. 313 (11HB-31. 313)VZ 4 12Z I (313. 213 - 13 13)yZ + (113113- 313313)00 dopB
et  divisa aeg. per 113. 113- 313. 313
palores ipsius
us astez h
fiet L 112. 112Vy313. 313YZ + 123. 123yZ(313. 313: 113. 113)100. 10opp 313. 313al = 0. ubi opott
125, 212,
==313. 313 (ab - ad) sit ab - ad = 3K 113. 113- 313, 3B
postiemo eodem modo ex aegque 10 et 12, eo
video autem nos indigere sex arariis. Et sane supersunt ad huc 112, 113,
pos ati renique binae si exalices p per. g +.. 4, quas sufecturas non quidem certum; sperari tamen
Porte sufficiunt aequationes quinque, nam in utraque aequatione tollo destinentur pp, et gq super
restat sequ. in qua q, superest, quae divellatur
nos lucrari posse si in aequubi est
et tentem
v, y, Z explitare per p et 0
Eut duae aeqgus. ubi p et q, harum ope tollatur lHamem aliaud
in duas, ita evanescet q, et per g habestur p. videtur
+. p +. . p +  faciamus pp  Kp + HK = . 9.
dextram partam hajus aoquationis etiam reddere extraribilem in indeter minatis
enque faciendo in altara aequation  ope duarum hypothesium habebimus aequationes
ergo Cietse bil (410. 111-
aro alterius valore  Ao2gqup+to+:00
vod saciandum : C11C. H 99 +: Q1o H0aa + = 21. Ho aq - u p 49 + 40 aa + . H0. 11 a9 -
209 +2+ 10. A1ag 110. tiona
420. 3004
1. 11aq + 10. Iaa,
ttrarenda ergo est radix extioor
extracida tulanda extraum. ex fiet rabium extraratur ex 10.109g
egi tote  us gerte qo eoster a saumuequete n perpose
Pito2, 410. 410 =
 109+ =na
= H2. H2L4
pretiot oit et Eat ursus modibunt si pro 4 ad ponas 5.
parabuntus vplore, duo priores
tinetur una
id
22173: 12 13 = quae aequatio dat valorem ipsius 223. Cui addamus priora, nempet et scriben
Remedium erit si faciamus
= 212. 223: 112. 123 (e
113. (13. 1l 113) Lta
(112 - 3
qu q2K)
u
qu
seu 112. 123. 113, 113 = 212. 223, 313. 313, ut ante) Ita enim patet cbi fore 313. 3cr = 2B. 2009
ex quo successu patet nos recte calculum instituisse
Retineamus ergo aequa
Rem
0 Itaque ex aequ.
o
1= 13. 100P
12. 11Z. 1
gI3. 112.1237
Espo y = 13. 812. 31 3. 0
10 104 no aquona
as i puliu sunt
ousaro. tropp LE1120qtopa
qu adoqu fina duas. 
10. 10299= 12010a9 = 120. 700aa