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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 340r, page id 00068196:0675
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sin fii pagine
olantus usus osides
praevideri potnt caleutum runque non succede
X + aakX + b = quadrato C sit X = sion su Y Y2oVYE + S3oVHI
seu opendio X= I + 13+ 16. Sit fomaula quadhanda 12(hq + B 1E6 + 23a 2,8 + 000B+ NI = C.
tiet es- igo 10. 20V 2. 130. X30B At 24
2. 900, EoV
2301. 20.30. 2,30.296. 3D
00d 600.. 2, 0g 120
120, 10. 21 V.
2.19 210. 20B A 2. 120. 130. 1oV 12E
sit  oi
Sit t = 10v + 1
c = 1t2 + 146.
2. 000, 230V
2 120, 130. 1
2. 000. 23a
2 (2) 20v + 21
6 = 30 V + 31
O = 14 Htrmob 8 = 160  16
Es D = 50 LH8 + 70V+I sit  XX + Aba = 00D
GB ru gotbi ai guat eto XX + A C= D8G: P Ex 8 explicalo fit a+ 22 15  intrdd 24ost.  B
t) = 10rovr ao ebr vut  B
2B = 20 3o vv, 10 11 V. + 231
00- a0 qe trirt e lib
1BD . 43.7. B + 10140 50V
1. Ho 70b 30. sAo. So V
i ng io  sis ode (H6
u s
2. H. 3. 10. 340. 50 p
2. 50290 3 40 G6 30 b (. 2 110340 1 G6
6010. 20VV + b 20V
00. 20. 30..
Geb - 115. abtriptro so (B0. 20. 21 V
2.001. 130
a
seu explicando
(t6 B 1070. 140 vD + 10. 50. 10. v7
30.70. 3901
2103052. 140. 340..
11. 70. 1e 140 v
31.70. 340
10. 71. 140.
30. 71.340
2. 10.34. 50.403)9.
3. 11. 30 50. 140 740.
U1. 71. 145. v.
31. 71. 348.
2. H1. 31.50.190. 340.
2.70. 140.340.
27]. 140. 340. V
ubi comparabimus primum
irrationales, inque eam rem
adhibebimus 140 et 143,
quippe in aeq. 9 explicanda
non recursuras
4110a+190b4100
Reducitur res ad hanc fauam ob tu ab 
et 220 a + 202b + 21 ab + 2104 201 b +200 0. jam ex
sin a, et b siuit 140 - et 340, desunt 110, 101, 210, 201, unde prodit aequatio
+ 100. 100. 230. 220 X
f 1. 120, 120, 200. 200
= 2. l00. 10. 290. 102
jam 120 _ 102
+2.190. 102. 220. 220 bb X  + 1. 102. 102. 230. 220 b (14
+ 2, 120, 120 200, 202
+ 1. 100. 120. 211. 211
+ 1. 111. 11I. 200. 22
- 1. 100. 111. 211, 220
= 1, 111. 120. 200, 211
( 2. 102. 120, 200. +20
2. 100, 120. 292. 220
11 110  10)
Spisinl 1050 n D 30. 50 5 (2. 70
+ 1. 120, 120, 202. 202
=2. 102. 120, 202. 210
4. 1. 11I. 111.. 202. 240
+ 1. 102. 120. 211. 211
= 1. 11I. 102, 211. 220
= 1. 111. 120. 211. 202
220, 202 211 210 201 280
avso 3Iso 1 osstrmatu terminus itta
100. 220 - 120. 200 = - 2. 11 2050b0 + 2. 410. 21.50b0. quod si hoc ponamus =0 fie
oy. 2
11. 20. Sed
et praeserretur
Eoc non placet, quia ita  et _ 2 revera quoad inefinito non se ab o
praestatentare, au licual tollere terminum (t. Nam maxipus etu
ubi et  C
foirt et 102. 420- 470. 20 = IL. H WX CCe - 11I, 11I. 202. 220 102. 120 211. 211 4 111. 102. 211. 220 + 111. 120. 2111. 202
Si abessent 1I et 211, id est si 70 et 71 essent 0. fienet
MI: mH . 1 = n BV1. 211 4 p.11I 2u  Ex aq uafica, D = (s ivomo-MeND + 2100. 1o2. 220. 220 b + (2 (,oL. VOn NOnOE b
+2. 120, 120. 200. 202
 noGA
10229- (26. 262
100. 12
+ in 102. 420, ut. 1H + n. 102., 20. 21. 211 F p. 102120, (11 211
= m 120. 202. 1I. M = n. 120. 22,. 21. 21 = p. 120 202. H. 21 et feiet posset deprimi aequata, fiereta
100-  100. 220 -1
102. 220 = 120. 202
+100. 102. 210. 220 = 102. 120, 300, 22D
+120. 120. 200. 202 = 100.120, 201. 230
Non debet autem s haberi
+100.220 102. td bb = 0 pure rationalite, seu
= 120.200 = o. 202 l-.
xoinciderent B
 se quadratorum (vel sattem quimdato Nane
parationes ad eodem prodeunt put 140
Caeteruum dubito adhuc, an sit consultum omitee
peculiau peculiari his seo culo
qui 
lo opamute aquec ue upentes es
parte rationali, cum Bodlatibus ex rationali. Praterea mimiuns
sed operae pretium ait aequaves efficiendas distuncte describere.
sen 1e0 vel 340 plioqui 100 ut 36