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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 50v, page id 00068201:0100
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Rem reduximus ad ff +99 = +2ab
et ffgg = fg = + ab siet ffgg = aabb
et gg- nabb ss = + 2ab - ss, fiet s L rab ff. + aabb = 0. seu f. f ab - o
seu f = + ab e f = 1+ ab et g = (B Hab
et erit 5f +gg 2F ff + gg + 2 ab = 0 = f5 + gg -2fg, erit f = g et
ff = + ab et f = V + ab = g ita erit fg = fabs et f5 + gg - + 2ab, ut oportet.
dy, y B 9+b, y+c
50y + al34
1= tad faD ay = a8+ aD + 1OD. B b ytC
yy + by +bc. fint 108 + 4u 8]  oD ~ A0 + g4 1OD gC +2810
SaOD, (b+C) 2 VOD
3 94 fit g= + d + asb +G; + sit et B0+6OD +b+c) (O, D bc ∞
compendio sit b +c = 0 H  et c = -b fiot 00+ 31 60
A63 (O+B,
fint  = 20n- D at e 60 + 33+ 50D b = 400 + 4 D + 803 seu 300+ 39D + = 0D t bb = 0
bc
Sit D = 100a na firt 3. 00. 000 + 3 110C 0 + 6. 10. 1 a ( + 3 N. H aa f 305 108 + = 001a0 t bb = 0
fiet 300. 60 + 3.10. 10, +2 00 10 = 0 et datur 10 et 3, 11. H, 1 a = 00 ev bb
fiet g = 20+ 2D, a: f ut 49= 400+ 4D + 80D, aa: ff = OD + W +6OD - bc
seu O (ff - 4 au) + DD ( 4aa) + (6f - 8 aa) O D - bc = 0 sit f - 4aa = ag,
fint  ag0 (+ agm Abag f 160a) OD - bcff - sit 00D = 100 + n a fieit
0000. ag00 + ag 10. 1000 + rag. 10. na0 + agnuaa + (bag - 160 a) 10 00 = 00. 110) = b1  (ag + 4aa)
dg 1L. 1aa = bc Cagiq A2) = c
fret 00.00 ag + ag 1010 + 6 ag0ul0 = 16aa 00. 10 = 0
denique rag. 10(ida = lbag - 160a) 00 (11) a  Ex OO fit ag  g = 16. a. 00. 10- - 8  tc. eva
ay = 20
A
00.00 + 10. 10 +5, 00. 10 510. = 10
seu (6, 10.00 - 2. 10. 1 = 00. 0ot 10. 10 (+ 5. 00. 10)
et dabitur 10. seu 3. 1 1 seu 3, 10. 10 = - 00. 00
quaeritur  gtb, ytc = Cto. sit u quadratus. posito summandum esse it gtb, grd)
Les summari debet dus tay, geb, ytc) sit ay quadralus sad +ta  = a C + a D + 2 a 10D
ergo su debet ytb, ytc, seu gy + by+ bc aequari quadrato tentemus casum specialem,
ubi b+C = 0 fiet  c = - b et bc = - bb et debet gu - bb aequari quadrato  et fiet
ab 00+  +  453) 1OD a (quadrato à  Q + f10) =) 94 + 258100 fiat 4 - 2 = (019)
60), bb
O9 a et 00 +697 =89+0
seu 00 + 37 +6OD-b1 = a a  u (015) + OD H. sit D + D = X et  = 1X +ua et 00 D - 20X rua
erit 000 + 30D = (10 + 20) X + - (1+ 21) a _ = 00 X fit a + 21 - _ et 1+ 20 = 00 seu 20 = 00- 10 et 21 = - 11
ertque D = (00 - 19) X - 11a et O = 10X - 1a. Et ex ag. N friet XX + 4∞D - bb = +a a xX + Oy sf,
sed OD =  (00. 10 - (0. 10) x  10. 20XX + 10 21 RX + 11 2lac = (00 -10) 1 XX - 10. 11 X - 11. 11 = (00 - 1o op X L 00 11 X - 1. 1
et hatemque (4 aa -1) XX = bb = t H, (00 10) 1oXX + cu rio  - 11. 11
ubi ut destruamus membra, fiet 00. 1 - 2. 10. 11 =0 seu 10 = 200, et 4 = 
bb Aa
seu 1 = ab  ab
et - bb = 2 4 - st, - 11. 11 seu 11 = d ana - f
( s5)
4 aa - ff = 4 aa= H, fit 4aa = ff seu 4aa -Hf = 0 quod non licet, nam fiecet
4ua
nam ob valorem I1, sublato 1 fieret ab =0 adde quod
si 11 = 0 fierent O et D invicem in rartione constanti
Ergo faciamus quadudum et fi 0G +9194, et fiat 00r m + 4  4(8+ 0D ~ st Bq + 2598 10V
d
507 - bb
ff0 + gg
pul  =  110D-6f 9= oX F na 3 - (00- 10)x - na
sed video etsi culculu procederet, tamen duci infire ab ita B in 5184 +9 spG, quod on licet
f O+ 99.