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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 146r, page id 00068199:0291
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sro formulis quadrato vel alteri potentiae aequandis
in indefinitis ad usum quadraturaam
a a + bXX + CX = a   aa + XXVY = a + LAAXXW + x Y
fit  b + CxX = 2aa v+ ∞t xX fit XX = b - 2a a:, VD =C
=bc + raa v + bvv - 2aav = B () B bc + vZ = E Ges. vZ + vrZy
le seu 2aa + bv - 2aa vv 2 f- bc Z + v2Z sed nihil inde lucri
sit  X = _ m + ny substituatur in a + bx + cx fiet sigraga
a +mnys tbungu tacmuus t Beny = _5 + 2fg_ + 25L NY + 2gh  t
bin amnus +6mi yy 4 4
CMA
4
+997Y
X) so + 11Y + 12H + 13V rutis
seu Abenn +2cnin = 2tat + 2bEm +cm Cf- to h - va g = n: 2 10 = 1. 2614
Ergo 11Y14 = 13So E N 14 + 1. = 12
An seua tbm tem + Bbnins + 4b Cntus + e ce m H = b p 46 cmmfu
e
a + bmm L cm+
ita ex aeq. D datur m, et ex a9. 0 datur n
4
um +mny Hunyu
Cm + 4mn y +6cmfnnuy + 4, m n’y + n y
sia
1 y + 12yy + 13 2 + 141
2gy F Est y
99yy + 2ghy t hhs
s = si0 h = Yi4
 = 11: 210 = 13:2 514,
11. H14 = 13H10 seu 11. 11. 14 L.13. 13
2Y10. 14 + 11. 11: 4.10 = 12
. 4. 10. 4 = 12 - B. 11.11. 12 + 11
2.10 16.10
seu (64)18.142 .91210 - (8) 10 tienit
In aequ. 2. Pro 14 substituatur valor ex aeg. 1. fret
e
5
(4) 103. 10. 13. 13 = (16) 122. 10. 11. 1 (8) 10. 11 4 12 + 16
= H0 h = si4 g = 11: 25 = 11: 2Y10  = 13: 3h = 13, 2 1 4 Ergo 11S14 = 13H10
rurjus 2Fh + gg = 12  Ergo 2Yi0. 14 + g9 = 12
99 = 11. 13: 4 f10.14. Et fiet
2s10. 14 + 11.13: 410. 14 = 12 seu (8) 10. 14 + 11. B3 = g2 sionq. seu set
64. t 1 14.ubis  pionsi posias
Ergo (8) 10. 13. 14 4 11. 13. 134
netior hee
ec
nittus
e4 )1P (2. 14  
auton
=13. 10:11
nimia exaltatio
13. 14 = 4 CCmn 13. 13 =1bcc mm p
8aCCmF Bmm+CCMF gCm qm) + 2bmibcemm + 4 Cr i6cemm A 54
 Exaeq. Dhit
quae dividi possunt per m
=8. bb M+ 64 bcmh +9b essr
sed ita video calm plane evanescere, et calculo isto nihil agi
nam  fit at = bb: 4c id est praesupponitur a + bXX + x essett a ibmenis
12 br6CM
Ergo gradu promtto, faciamus: X = in +ny + pyy,:, q+YyY
q ergo quadratm excilandum a 20 +3y + 229 4239 +t a ist.
2. 1 +(2, 20. 217 +(7. 20. 22yy + (2720. 2393, (2. 2024 ist
+ 2121 +2) F21. 2E +(2) 21. 23 +(2) 21. 24 1)
2bbm bemi
2232. +(2. 22. 23 +2. 27. 241)
+ 23. 23 +2. 23. 291 + 24. 24y
+14 y + 15 y + 1b9 + 19 1 +181)
a et fit 1. 11. 18. 118. + (4)16. 18. 10110 = p7. 19. 10 H0 + (4) 18. 12. 18 Y9 Et 1(410. 1217(8)10M 18 = 12.11 17 +(8) 10. 15 5018
10 + 1 y = 12 yy + 13 y
ete
(4118. 16. 114(8)18. 1710 = 1717. H +)18. 13 11018
o eaand ntas ia tum intua r alende duo priestiam aotunde
(4)10. 12. 17 4(8) 10. 1.6 tioc pedsistunt hontvatles, et mnbibantum hontuot Arormate, et pants ante duo series eotu motanda