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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 85v, page id 00068198:0170
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Quadratura altior reducta ad sonicam
= a, t a fiet X = a - a y,: y se X = aY a) a y 7
(B = a:, X + a fiet Z7 = a a v,: v bu Z- a a v.v
atbus + slemus = co fit a +bus lxmu +2 satibus, lamus 2) r
Aey, nepus
cteu utpus
et co + ae + 2by + bby4 + (2 Ulmytn - 25 at by 42Cd (+ my 42 an, camus
sitit addenda
utpis
C+2C ey+ eegy n+ inputppy.
arbus, lamus
ntpis
etey
(0 + SD = co fit  O + D + 2S0D = W0 et 40D = at + O= 5  = 20D4 - 2. 20D
(4) creys, ntpus
seu fit O + D + c = 205 + 20c + 2D at pro O pribamus 0: 6 pro D scribamus D: E. fier
+(32 ∞ et Oet + D6 +964 20096+ 2086c + 2D86 co sont  atbus 6= ct ey D= Lamy. P.nt
fiet an tap tan + bny
P3
cl -
-
6
63- 05 =0
Bpgy =0  seu bp = em an = cl seu p = em: b n = cl: a
et bn+ ap= elt em, undetollendo pet n fier
vel: a +aem: b = el + em seu bbel taaem = abel tabem
siet mo m bb ccra abetb
quibus valoribus ipsamur n, B p substitutis in D. 8 fiet = l + abel bbl y,: cl_ + em y
et fiet m = bbl abe l - bbcl, :, aae- abc
ec et +acel sy sed ita moncratire e nominatore divisis
per ael -bel, sit D: E = 0: 5 contra intentum. Ergo sic tollere non licet, ut deprimatur, aeq. 2 ad coct
seu 3: 8- aaet abet rat da et Y   3y: +
 videamus an tolli possuit termini in quibus extant s et is sed ad eam rem opus foret aequationibus
ascititiis sex id est consunterentur omnes literae nostrae, et fortasse nec sufficerent
s estet si redemmus ad aeg. O2 + D + cot = 2OD + 2O CS + 2 D C et faceremus  atbytcyus
et B = l 4+ my + ngy et cd = V, r+5Y+ non tamen habtiemus literas plures quam ante et
nitilominus ascendemus ad et yt. quid si faciaamus C = a+bus ei D = l+ m y et co = v Tresy hoc
posito habetimus n ita ut detur satbu + VLAmu =  v seu tarbus + stamus = v Trtsy
aa + raby + bbyy _+r tersy + Ssyy v = + 2aY + 2a5y + 2b5yy
Ita ex O + D + c0t = 20D + 20c0 + 2D cot fiet
U +2lmys + mm yy
=2b m yy
2al-2m y
=2bly
ve
+ 2 b r 1s
+ 2F + 215y +2mSyy)
adraturas Conicas promovendi
mi
o altiores, cum aliqua genealitate. Nam si faceremus 5 =0 non esset
a
quadratura ionica, sed quadra tura absoluta
aequemus hanc formulum generali simili
4. y neyu + igrv + 29ne royy er
∞ 16 + 15y + 14yy + 24vD + 23yVP + 22yyVV + 32V F 31 y V + 30yyv = 0
sen Y16. 19- 15,
et coparando fiet: a - l = Yi6 b - m = v14 2ab + 2Im - 2a m - 2 bl = 15 C r - (25, 5 = 130 31 = 2130. 3
et a + 1 = - 24:2 et b+m = - 22: 2 et 2a + 3 + 2b+ m  = 23 sive - 24 430 - 22 132 = 23
(a = 2116 -24 l = - : 116 - =24 b = 5 114 - 1 22 m = - 1, 4 - 2 32 r = 132 5 = 130
15 = 2 +14. 16 31 = 2 (30. 52 23 = - 24132 - 24 10. Itaque tres adsunt cestrictione
perinde figun alquam aquatio est conice Quadrani potest Figura ad quam aquatio est
16 + 2 s. 4. 16 y+ 14yy + 24 vv _ - 22 So2 yWV + 2yy V + 32 v + 2 130. 32 y v + 30y vt =0
X
poro 4
nam fit pelle
+ 2. 16 + = H4Zy
-+ 4 222
132 + 130y
(.Hib  LVy
+ Y- 124 - 5 22d
t conditiones, possumus
32 + So
introdue y, ex pro a substituendo ny +M. ubi _ arbitraria scopo inservit  C
intreducere y, pro X substituendo mytn, ita duae nobis occurrunt vibitraria. sit scilicet
se ab + 45Y + 44 gy + 54 vv + 53YVV + 527XVV +62V + 61XV + 60XXV =., et pro x substi
tuendo n, fiett 46 + q5u, 45nY rAnnyy + SAWV tSSRGBB + SEmHyVB F BLV L binyV + Sonnyy v -0
seu
eu
62
+45m 2 +244may
44 m
+53nVB L. 52tiy bB
+58B VV
+6.m  tabo mug
+60u
+ 15 y + 14 yy + 24 vV + 23 y VBF 22G9 VBF 32V 4 31 yb 4 30 yyV = 0
16  15y + 14 yy + e4
16
et ob 15 - 21.918 et fiet (2) 45, f 2. 44m nn) = . 46+4 5m + qamm r 44 n) et habetur M
Basteruirgharum
iga potestl.
ob3- .  - vel ob 31 =, 10. 32 fieret  1 61 + 2. 60m (2n) = 62 + 61 m + 60mm 4. 60 (i n) unde etiam haberi potest H
ob 23 = - 22132 = 24 130 fieret. 8853 m + 2. 52 mn = = 5Enn 162 + 6, m + 60 mm - 54. +53n L 5 2 nn n 160. Et
ila habetur B, et proinde unica saltem restat determinatio, seu
fit
53m + Z.52 ma =  C = 52 nn, 61+260m - 54 + 53n+ 52nn I 160
ut indagemus n, biet 452 (+ 4. +5. 44 m + +. 44 mm) = 4. 44. 96 + . 44. 45 mt (4. 44 mm. Itaque evanescit n
M, seu res redit ad 45. = 2 144. 46. similiterque ad 61 = 2=
itaque posito m = 1
fiet XL e 51. 6) 1_ +C0 Et ~ + 2. 54. 6d 4 253 6ON, adeoque sit n = - 254 60  52. 61 + 253
sed in aeq. ultima haberi potest m plane, neque enim licet facere n =0. neque etiam licet fatore m
e
estant
di ones datit a i e ecurs a
sicetores oie ane ntus ao erei
relinguere utcungue vel assumerer  nere qo ita aegu
aa bb+cC,
2ab- 2ac. 2be
non est extrahitit
1
unde res hucrda
e
etey nepys