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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 215v, page id 00068194:0430
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1qu:
13 gX + 10yA 31
4X + 5y +6
+6, 19X 4630y 6, 21
6,4
15, res +5, 2.
rpoB . 5. .
+4, 16x q io. taut
10 X +ACyX ,qu rAX + 2ay 4
=4.. - 45
11X + EH + 3
e+1x+ 2Y 41V
+ X + 5y + 6 5 aequ GX + 20 Y + 21 + 6. aequ. 6.
 +6y + 21
aequo
comparando D et D fit: 6uequ. 45 per termmos ulrimos,
et 5 aequ 44 = 2 4u p 2, d. aqu. 23 - 4919) squ. 23, 21, - 45. 19
21 -45 ix
2i- 45
ubi comgrendii carsa faciendo 45 aequ. 21, 48.
fie
212 - 45
5 aaqu 44 aere. et 4 aqu. (3aequ 24 - 620. et 4og. 23 -619
Rursus ex terminis piniis sabstituendo n, sut.
121 - 6
4319,, 6, 19,  - 13 + C,45 6, 19 63 st . 40
DX + ZWX any +25X + 34y +35C
_ F+ Z + Z, 12, aqu. 30+ 32831
erg 14 2 aequ. Y5F HIB.
aequationebus substituendi in ae termmnis a. y. est
hinc vatore insius rrgs- 4 substatuto in X fit:
4 aequ. 40. serovalore 4. substituto 43. 6, 19 40, 6, , 21, 8-6
34 10 aequ36..)
3 70 aequ. 37
et 102 aequ. 31. 1equ. 3
36. 3.7. dutre artitharia
1. aequ. 34
ti diatibari 18. 1’ aqu. 3 a qu. 30.
Datu quantitatum summa
2+V aequ. a)
 ex +5y + g
Atex alitu  R.ho
AX exy (ny +EX +ot +g.
omparando: hoqui L., laqu 5- 2 f. rastus l aequ. 
2 aequ. 34 equ. 32 ehoequ. A. et
F. Nagu b aqua- 2 2.
euatntus
Ergo A 
e A ehs
St1 aequ. 20. fiat 20  ter
x j 1920 -t aqu. et + hl
et rux y - a) ab aqu. 0.) rgo efarqu.  efs Bl aqu. e 
seu  b ago ay- y
auo
fl aequ. 12.
itur eth per fl. fit: et  el + hf + hl p 19, 20
eh A aequ eA. Erga e L
24
2126  48, 2. t. b, + 47, 619
hX + ly + m
 infy mus
Hexy +LF y
+ 19.
et rectingulo invenre, 1,t aequ 3053+ aequ 3L) ethaqu. 19. dete fatia (9  A qoadralis
quantitates.
xy aequ. b2
fiet
L 22
2-6
qui valores ipsarum 45 substibut possunt in
F Ix + 25, 2 xy   Y + 1,3 X +21y =8, 10) et quia L9 - a rqu. 43 - 4, 21 per. X.
P110 820
 aequ. 30. 2 aqu. 32.
D,10 aequ . 35
13-4 41
et hl aequ. 19,20 - 7
melius: n aequ. 8. laequ. 6 = 58 vgu. 2 - f
 sid ecionto circadumuum belut dumetum h aequr  e f aqu. 20 - L rgu. 20 19 + 5g
sammum descripto
apolietur qulaudangulos rectos  ergo posita cempendit carsa  aequ. 1. seu d  qu d fiet d aegu. 20, 9
radix rectanguli
diametrierunt
fiet Lingur 2 et S aequ  .
 quantitates quasitae Ruitus h aqu.  = eg. et h equ.  19 - es. erjo posita sucqu. 92. f
eodem ado ut ante. 1 aequ. 19, 9.
y- ay +a rqu a V  manentibus adhua f. et RC ad et ex X. fiet 1 d aequ. A. seu eagu sig.  Dr9
sergo 59 - f9 aequ 20,9 af 9r seu ov 9- 20,9
C. 3 aequ a -26 +a). seu laqu. 209 = ag. Eodem modo e aequ. _- 1991 et h aequ. 198 1189 d qu
ego pe. X. filt Aaqu he. aequ. _9 - 19 9r7 198 - 09
9d
et per y pei ( aequ lf aequ 1g = 2092, 208 = 5v 9,  er 5ug. 1 89- 199 e0 3- or9, + 29. l09, 198 209
9 = 9r sis
d= 9u 
compadi causa ponatur e aequ. - 9. fit. lagu. 102o g 2 a. haqu. 23 +8
Aaquhe aqu. 19 9 - 
3= grE
ful
+g. poulsqpu e srae  aq.  10g- a e aequ 439 9 - 
29)
 Sequel + fM aqu. 10, 20, 9 (+ 19, 960 -  10.9 2) - 10r, + 19109) ( 20. 910  19007 - 00 
ey 5 aqu. 19, 20, 9 - c06v
292
notandum auter 49.
posse, nam ptor eto
ut sit 8 aequ. - gr. sine novis arbitrains effice
am in aequation
ex terminis crbitrarius st
jam: + 30 X + 3, y∞y + 32 g + 33k+34y + 3
nempe
+ AX = 3ZX + (n y + 2X, +60y + 8
X + ny + ~5i
A
Xy +8 V+
qu. 194 +207 .. ultum minu unus
in ribri punt an
ubi sunt o. 7. Z. resc. dutae.
313  etc. et .  et. abitieri e.
sunt autem jam inventae: 38. 3. 35. et X. E. . et fief ex qualibet formatresam terminavinus,
et aequando valores fit 30 aequ N - A. seuam 2 ( . 0
et
+33: (h aqu. B aequ 24 (N- 200 1 + ar.) 20 el
seu termini alte
debent itemr
i
30 aequ  aeqo Xe -R.  3I equ.
Ubi rurs elegantisimo compendio in omnibus his
ascendentes si modo pontis 37 aequ. 49. den 37 aqu +29. itaque per
.0V inveniri
7 2
est
Eubus destiitur  a ov
demu fit ex ultimis teminis 35 aqu. 51 + gr. Et sea absolita est comparatio quanuanime potuao alis
inven
inventis .0
1. quod fiet ipsam, 29. vel 3 inveniendo
g. hop