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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 175r, page id 00068201:0349
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b, yre
(20)
Et his vec- 
si vellimus facereagu bu= quadrato, possumus fucere nu - qra
et ytb, ote etiam aq. csto unde necesse cnt vel yb, et ytc a quodlibet singulatiu
aequari quadrato sivel unum quodque aequari quato facto ex quadrato proprio, in formulam communem
Ad hibetimus etiam Ldlm et  Lrl. Xon et txem. X.n.
yel sit 10, _Am sit 20, et nen sit 30; et similes quantitates per x et Cognit simplices per X, conti–
undum e
Eateris sit jam lay = 12 so 20 + 113 f10. 30 + 123 + 20.30 + 10vea () et quadrando fiet =  a r esse roigna
18o 100. a a
di
212 f10. 20 + 213 sio. 30 + 223 120. 30 + 200
= 2.30. 113. 123 110. 20
1. 123 s10. 30
o 
. 212. 212. 10.20 4 2.30. 213. 223 11020
ad. 22. 207
6. E. 2
oei a ins ad 3+ b. 
Odate
erit y+b, ytc quadratus, si
Eme
neta esit it compendii causa
neunt literae sequentes, ita pro 1120X + 1121  per compendium scribamus net, atque ita in
et a, (5t) 112 112. 10. 20
. 122
2
simplicis, sed  gradus compositi, ut O et )
10. 3c
es 93. et itn yse qudut)
Pieid , e eodem modo grlv)= OBa+ DBC: 5D
G: DD. ubi 6 et e sint gradus
quaelibet autem it t nota , 6, 8, 8, etc. continet
formulam quam ingrediuntur h0. 20, to s10. 30. +20.30. It ex 7 et 9 fiet 00a + DD 588 et
30a + DDc = 88 88f
 pro a inaeq. u vel1r scubemus E, fiet Dh + 33b= 58 et
eodem modo et ex 12 fiet OOh + DDc= 28. 
Ventamus jam ad aequ. 1. actu ipso exhibendam, ut  quia pari jure et modo deinde procedi poterit
cum aequ. 12. sit 
fit 65  312o. 3120. 10. 20
0. 3C
3230. 3130. 20. 30
300.300. a a
 (13tro) 6 = 312H0. 20 = 313 1o.3o + 323.120. 30 + 3000a ergi quadiundo
+ -303130.3230. 58. h0: 20
2
323 110. 30
0
et (15to) 8 = 412 ho.20 L 413 Y1030+ 423 12a30 + 400 a
sed quid id prolixius fortasse sufficiet facere (3to) tay.
(5t) Z = 1.22
90.20
unde feri test ex i15 fieri potest 568. quod
comparabile cum 03h + DDb g ap. 31.
112 10. 20 + 13 A2o 3 a = (41) 3a et fiet
21 110.30 + 200a
= (610) 3B. et quia (3mo)  yrb- deo vb.
et (8V0) ytc = Odh + DDC,: DD et  multiplicando  yt b per yte fiec gG+by + bc = B (6t) OYhh + 00DD hb + D bC: 5+
et debet fieri quadratus numerator fieri quadratus, ita tamen ne sit b = c
It C 4 -
+ 1234 30. 30. 20. 20 hh
6. 112. 125. 10. 30. 20 hh
LM
bc3 = 2137. 10. 10. 30. 30 bc
2007 at
4200. 213. 10. 30 bc
h(b11) OD, 12. 21710. 2030
123
123. 4330. 20.10 F h ete)
112.200. 1026aa
123, 200.30. 20 aa
4. 112. 123 2l5. 200. 10 20309)
a
4. 112. 1233.3020 hh .. . . .
4. 215. 20ca lo. 30 b. (10. 30
4. 213. 202 bc
2.112. 213. 20410. 20,
2. 112. 13. 200aa 28)
jam exts erit
99 = 112. 112. 10. 20 = 2. 112. 123. 20 s10. 30
3D = 213. 213.1030 +2. 213. 200a L10. 30
200. 200. aa
1 pro 10n 20. 30 scribatur rectus
=. SIto a 4. + si to 30
2. 125. 213. 2ma. 30. 20 y hBrc) 10. 2
2. 112.123. 213. 102430
173, 123. 30. 20
2. 42. 51 110.30
112C, 31 ut appa
appareat esse grad
Si 112 vel similes sint constantes su 5 sint 120 seu contineant X.  assurgetur in Memoro ratio-
42. 42.
nali ad gradio X unde comparatitiae aequationes 5, et in irrationalis vefficiente ad gradum
S1. 51. 10-30
X, unde compantitae 4, summa 9. literae assumtitia, in A2 sunt 3, in st sunt 2 in 10, 20, 30
erunt 3, ex 112. 123; 213; 200 sient saltem 3 summa 11 vel si velunque negligere
apsas 112, 123; 213, 2 lanqua aequales unilati, licebit in ipsis 10;20; 30 assumdre 6 arbitrartas
et fient itidem H quod posterius est maxime spendiosum
sed cum haec sic sulis sunt prolixa, redeamus ad Methodum magis anclyticam
et videamus primum un liceat d0h + DDC aequari quadrato ege et facierans
OTh + D L -c in OTh - D t -c = 9Ze sit e = 159. et faciemus C th + D sc = GH et
similiter O s  D L.c = 8 Lg. Ergo O Mo + D F C. 5) = O M: 9) - D A c.9) sed ita O et D datio ict abe
sit O = n2 tro. c0 + 43 troo + 1y t20. 30 + 100 et D = 212 toro + 217 l1o. 304 223 fro30 + 200,
fiet ac th. s) F 212 H c: 5) = v2 sib: 9)  2n H(c. 9) seu  212 = 12 (. 9) = H h. 5)): ( f(. c. 5)  H c.g
Ergo altius assurgendum  Non ergo licet ODh + dDC aequare quadrato, si tam O quam e sint
ssimplicia. sint jam ambo composita et fiat 00 (C) (D) h + D D (2) (D) C = quadiato P2 (2) (8) 1sg, et
fiet OD) th + D() S.c in 0)  O (0) Ih - D () L.c = G (9) 1g
ubi ob ratione
jam dictam non licet facere O(D) th + 3() tc =  ipsi C (0) th = D() LC multiplicato per datam
itaque oportet O(1) Th. +D(D) S.c aequari quadrator ia  ob ambiguitatem simul utrique salisfilet.
quadratum sit  popq f. veniendum jam ad explicationem ipsorum O, D, (0), 6 4. sit
O = i Sio.ro a 113 sio. 3o + ag 120 30 + 100 a C(O) m. 2n 10 h6. 13 er. 30 0. 20
(C) 2n...
(1 op
2
313
323
623.:
523
Contrahendi calculi cousa forte licebit facere 1 
113, 213, 3(3, 613, 100, 20d, Loo 600;  Si 513
0
3) = 6u..... 6
500.40 +513 l1830
demva
00a
e
vinque
V. 10
123.0ode.
100
as 104
idem calculis institmetur, 
pro 1, 2d,  potis v, 21. 31
13. 213 1
an 1020 + in v3 20 l l. 1 3
123,. 223. 302D h
ien oret 3. 6o.
IH - S13 512.  316 + 2 513 costet sia30
500. 500. q 
513. 512. 1s
313. 613. -C500, 500 15
M au et X on. mp) S  I
123. 23 . (ih 313 biy (1 1. C 2.500. 500. H sf
1it n h 3 3  135
8
3b = L 131
unius et secund
X; et pro _2 et
et similes potest
scribi 1120. quia
possunt intelligi
gradus uleius.
Hoc, et pro 1t ponatur 1, et
pro Gs ponatur (G) et pro 500. 40, 2
ponatur 100, 80, 81
+
ng
pu
mm  iol eoi
aota in duta tete quroa e ti ti an tatre siili t ab dproc
cea
123212. 21 Th 323. 612. 21 Y.C
175 C2. 813. 00 quos
equationes oparatitio 20
num
a2 lo2  2 B 20
atere
123. EE1b 523.612= 55