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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 336r, page id 00068196:0667
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Desideratur ut productum ex tribus xed, x X +b _ XtC, Xid
aequetur quadrato: ratione apta t ad quadraturas, seu ad efficiendum, 
(DV+O13,
habendum  Sontb, XtC, XEd dx. sit ax = 6R et 40 + 9. V + qL V + e t2
 et O C quo 1H V + _130 146. et 8= CoV + (v  mitio (S hores 
et (B5= 112o 4, + 53201852
01v.
2v
at
s
sa
013o v 7b
0131VS
1
82
2AdVHts
241.1
19
 10V + uV 2 = 20v + 21V. 
1 =44 00 =  = 36, oc = 2. (6.  = 2. 20.31
in proq
ponen
q0
ibus vntantis omnibus ase
(
230HSIV
Ergo sp. 10. 11Z 10H. 3. Ergo 3 Si. H ut 30
4
su t 3010 s ita 2 1 si.
ALeOL
At ∞Y = 11. 11 - ab =  4 31.3, -  seu 11 = ad
ergo finiet ab = ad conte Hypothesin  pat 
quare six
rem redinchoemus. Maneat aeg d, 255, 6,78
fiet vol 10. .10. H O2 ab o1302, 19 o131. 1
excit a sit G  - 0 t Ex aq oriuntur aegus. coparititiae co12 12. 1514
00 = 40. 40 + 4130.10. 30= 50. 60 + 613010. 30 Ex aeqi9. omutur 15, 6, 17, 18, 9
lle
O1 = 2. 40. 41 +  4(30, 10,31 + 11. 30 = 2. b0 1 + 6130. 10. 31+11. 30
02= 41. 41 + 415. 11. 31 ~ (et 61. 61 + 6130. 11. 31 = b ad0+
01307 2. 40- 260 01 = 6 Ergo 60 Z e ar 
ab
O130 = 240 430= 2. 006180enr
61 307 6120 =  q0 4130): 60 = 41 (4170): 61
O131 = 2. 41:4130 = 2. 61. 6130
sadt
1=6
0131= 14 2  = 2. 616130
(au d Mb:40
(2l
Ex 15 et 20 fil 40 + 4139, 10. 30= 60 = 40. 4136266 Ex i Ex 1 et 20 et 22. fiet similiter
a1. 91 + 4135. 11. 31 - ab = 6860. g: 40 + 40. 1930. 11. 35.60- ad
Et ex 16,20,22. fiet
Ex ∞q. 23 fil 4130 1607 -40, 60:) v. 30. 60216. 30. 40= 60 60. 2 At ab. 60, :, 11. 31. 60 - 11. 31. 40
2. 40. 4 + 4138. (0. 3+11. 30 = 2. 60. 91:40 + 40. 430. 10 ur 11. 32 , perq
2
quae aeq. 27, deponm habet communem divisom noratorum, et fit 60.  - 40. 66, v. 31 = 604 - (. a 41 + ab. 5.  10. 30
te
mosex Ex 2b etiam fit 4136 60 2s10. 30. Eo ipsy es fil A 2  A. (  2. 414 00 - 40 = 109 1r11 2060- 46
seu 242. 10. 30. 41. 602 1031 + 11. 3, 40.  seu 60 = (010.2  2 40. 1054 11 30. Ergo ex 2E et 31
fit  = 10. 31 + H1. 30:, 218 30 quod mihi suspectum. Ergo calculum osumemus
qui s rectus, tantum opus est tolli 60 ex ag. 28. C1t
axil =  00V + 0i v +0∞ v. + 013ov +013 N (h6
abulad
ld
O6 = (8 + quqov tuo qiv + alsIV +Z Mor p n or Hit
viro
0. 3 cum opus sit tantum ad
(10)  e (15)
435, 10. 30 +aigoiog + 4190 )1 31
00740 +4130. 10. 30 = 60+6,30. 10. 30
ol J.1B 41, +13O10.3Ituso = 2. 60. 61 +613010. 31 + 1130
o= 41 4128. 1. 3 ab= 61 + 6130. 11. 31 - ad
015o22, HX. 40 26130.60 E 6130 = 10., v. 30
Q= ut 10 tantum  pro charactenota 4 ( 013t 2. 4130. H2 2.6130.61 
va
(9
C2
Ex aeq. 18 fit 6130 4130. 4: 60 Ex 19 fit 6130 = 4130. 41: 61. Ergo 43: 41 = 60: 61 seu 61 = 41. 60:40
 initio numeri ponendo (, ut pro. 430. 10, fict 613060.
(
Ex 15 per 20 fit 40 + 4130.10. 30 = 60 + 41,40. 560 10. 30) Gurpercont n, fit 45+ 4130. 1. 31 - pb= n. 60. 40 + 4130 41. 60 11. 31 - ad
Et ex 16 per 2o 22 fit:, 2. 40. 41 + 4130. 10. 31+ p1. 30 = 2  2. 60. 41:40 + 4130. 40: ( 1031H11. 20 Follamu 4130, fit nod
Exaequ. 3 3 sit A136 =63-40, 60,: 10. 101- 40 se 13d 6   Exaq. 24 b 41 b0- 40 + ab- ad 40. 11. 3160- 9
seu ex depresfier fit 60-40 , 11. 31  50- 49, 41, 10. 30 + ab - ad 40. 10. 30. poroo ex 2b depos fit H3 - 60:, 1030
Ergo exaeq. ed sit 24) ( ) p 21+12(C 4 2, 41, 60(60-40(60-40740, 10. 31 + 1139, 60: 10. 30
cntus in aeq. 30 fult
41340 10. 31 f 11. 30,: 2. 10.30, quae aequatio vatis facit, pria
falsus. Superest jam aeq.  iqua moas substituatur vator ex ertirt os qu C 11 seu ( demes
a
sib o Co p  4) 60 40 + 40 ab- ad i1. 31,60- 40,  10. 36 m  18
evanescente 60 fit
41parilfit (40) 1o sit11. 502165. 4d + 10. 40 (40, ab. ad 2 4. 10140, 1. 31 (1) 60-40 seu
fit A 1 45 ab ad, : 66. gd q 1. so. nst  pmu 1d uti si faciemus 1ontt So= v0go 1 31
fierret e  0 4 2903040 rabuad: 100  et haberetur b0, sed 40 maneret
arbitraria ubi tet 60 et 40 serve et respectu ab ad servare rasdem teres, ut si pro 60 substi-
tuas 40, a et contra, et pro abs 60, a 40, abut 4b et ab substituas 60 et ad; et vicissim,
re natio qa ante quod tamm non apunt unde uisa cluitus huc sutrecta
ermem admillum in aeq 2C ubul scrintem eo 3 6o 1d cum sit scibendum. Unde jam 10. 3le11.30 = 1on1 + 11.3C
revem  esse
+2, 10,70. 11. 31
Ergo ex 33 per 34 fit 10.31 + 1130 =2103] 8130, 68.40  4.10. 307ab+ ad seu 10, 51 = 11.30,: 10.30 1, ab+ ad:, 60-48
quae aequatio revela servat leges homoeoptotorum. Id est si permates 40 et b, cum 60 et _ d, nihil mutatur. quo in quo
aliqua calculi comprobatio est
sit 9120 40 2 + 53 O. 30. 203 =00 et sirv.m2t + 53E. 32= o2 + ac et s12B oatta. 2  53IS. 50.  B
2.5120.5320.20 36130
 ja ingentat
Pt
et 201
Habemus ergo 21 per
et sO= 00, 0.co 3316 . 10 ortac  uns -55ib t sit. 51 26 =-002 E1 +D taC. 30. 20, :, -10. 203(21 3a
2,5120, 5320 219131. Ex 42 et 43 fit 21. 2620131: 0130
Et Ferruc. r,   3. D-00.1. 21 407 tac. 10. 203:, 9u2  2 - 30. 20. 11 21 F 10, 20. 31. 2
c a stind  Es. 1 idi v
si explices
p0. 11 714 or tac1o. 20 30. 21 + 31. 203 01. 30. 24, (10. 31 = H. 3
 er s  ter ue ae
u. 4+
31F
i
 arte ie tie ti