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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 64r, page id 00068195:0127
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videndum et an ope rectae et someae datae problema solvi possit
componantur aequationes 1. et y. multiplicatae fier:
Ida fpdaX =Gay 4 qu xy
+2aX
+ tax
+ 9xy
 (15)
7aequ. 0.
+ + a xx -+770
sumamus jam aequationem ad rectam: 2X +3y + 4 eamque mulliplicemus per 5X + 6y+7
2x + 3y + 4 aequ. 0
+27X 43,77+4,7
2, 79 (3 B Y7  1467
+3Sry +4, 5X +4, 6
comparentur aequatio 16. 17. fer: Cr
UrTuVAByx +y +16 lequo
(16)
2,5X +36yy + 26Xy +2, 7X +3, 1y +4, 77 aegu. c
Fx+6y+ 7
b Egu 1 bbex bXx aequayy e t) x 14EX
Habemus ergo C. Z. 7.
per aequationes planas
b, y
Ecequ.  haequ. 12 4 aequ. 16
26+3, 5 ae qu. 13 Ergo 11, 6 + 12, 5  C2
(2
(13
ua
3, 1 +4, 6 equ15 Ergo 1i1 + 16, 6 aequ. 15
17, 1615 ae qu. 14
(15
126)
2,7 +4, 5 aequ. 14. Ergo 11, 2 + 16 5 aequ. 14
ponamus 6, aequ. 8. fiet 11, 8   - 138 + 12, aqu. 0 ex aequ. 21
2 aequig. fiet : 12, 9 - 15,9416 ae qu. 0 ex aequ. 24.
Z aequ.to fiet 11, 10 - 14, 10 +16 aqu. 0. ex aequ. 26
jam exdatis 8. 9. 1d. videamus an dentur 5. 6.7.
(31)
(3)
quae aequationes 27. 28 29 sunt planae
8, 9 aequ. 10.
CBBye 
Ergo res non procedit Generaliteo sed eo solum casu cum 8, 9 aequ. 10
per aequ. 29. habemus 8,9.  quod si jam ica componere possumus aequationes
27 et 38 ut dividi possit compositum per 8+9. vel per 3.9 vel per 128. 17,8+ 189
habebitur quaesitum plane. + 51, 82 - se 138 + N 12 1(3
equ.
+ 7n 9 - 315, 9 + 716S
i jam Xe t 71 Sen aequ. _ - 212 et 513 aequ. + 315 et 5 12 + 716 aequ. 0
haberetur 8+9 vel 8- 9. verum atque s ita ob dat. 8+9 et 8,9 haberetar
89. 8 et 9 ad huc semel. Verum, quia jam tum habetur, satius est omissa
assa compositione per aequ. 27. mo 28. investigare, 8 et g. atque inde deducere
8,9. et duos ipsius 8, 9. valores conferre. quae collatio si procedit aequatio
je erit ad rectam. facile autem erit, absolvere calculum:
8 = 128 + 12 aqu. o. ergo 8 - 28 + 15 abt 15 812, 1.. Ergu 8 49 + 13 4 15 (. 4 
(2)1
D 1 (4) 12
et  aequ.  15+ Si - (1218. et 8 gequ. 10 aequ. 12, 15 + 13 Sis = ()12 6 5
(2) 12
et 8,9 aequ 13, 15 + 135152 (4) 12, 16 + 15 S13 (4)11, 12 + (13 - (4) 112,  152- 4) 12, 16
(36
() jam
(4) 11, 12
jeu 8, 9 aqu.1o, et 10 aqu 14 + S14- () 1, 16
(38)
equ.)
Oper. 33.9
Ergo duos ipsius 10 valores ex aequ. 38. 37
inter se aequando, per arbitrarias quae super sunt, habebitur quaesitum.
ed satius erit vitare irrationales, hoc modo
loco aequ. 29. scribetur n8, 9- 14,8, 9 +16 aequ. 0
pro 8 scribatur valor ex aequ 27. ilem pro 29 ex aequ. 28 fiet: Vn  H, 2 8 - 1
H  1n. 8 - 12, 15, 9 - 16 - 14, 8, 9 + 16- a qu. 0 seu + 13, 15, 8,9 -
12
Ce2)
14 8,9
ubi posito 15 aequ. 0.  (quod in aequ. 17. Non difficulter asse qui licet) tunc insigni calculi
compandio fiet    F,  9) aequ - 12, 16. seu 9  . 13, 16 et in aequ. 28. Scribere possumus
44
12,14 (45)  14 duosque valores 4 45
(12,9, = 1316 seu) 8 13116 9 ) + 16 aequ. 0 et fiet  aequ
 geralo ad Conicam
  po recam
aequando, habestimus = 13, 16 -13 5 aequ 12, 19 itaque si in aequ.
eftice cotast 15 aqu. 0. et 1  13 16 + 14) 12 aequ. 0. 3 abe bit ae quatio n fetan
y+  aequ. 1
5ap s
aequ 3
4 aq. Bs Ap