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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 23r, page id 00068049:0045
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Ad dimensionem c curva Ellipseos aut Hyperbolae requiritur qud
sumum omrium y= Saa +bXx
aa + CXX
qudtoscalitur a geadraturms rutionales
seu y= Saa + bXX, aa + CXY. Quae revocabitur ad quadraturas rationales, si possit 
C
aa + Cx
ebeclecet
Quadra e
extahiradix ex Caa +bXX, aa + CXX seu ex a + baaXX + bc X
2) compendi causa baa + caa vocetur e et bc vocetur h, ergo a + eX X + 1 4B caa
a
 a
quadrato
compendii causa (() sit B+ c = e, et bc- h, fiet co + ecob+ h v  quadrato  itaque debert
Y et co  inveniri in integuis quo ad indeterminatas. sit v = 10 + il n + 12n F 13 n + an e
et C0 = 20 + 21n + 22 n + 23n + 24 nt et et DC~
quibus Valoribus substilutis in aeq. 6 debet inde fieri aequatio identica. Sed sffecerit rem
antabimus intio in brevissime hypothesi, ponendo v = 10+ un et c = 20 + 2n et
9= 30 + 3in +32 n firt c0 = 20 + 4. 20.21 n + 6. 20: 21 n + 4. 202P n + 21  +
10 + 2 10.1LN + IIN  exaeq. a R, COB = e1010 +2C 10120 A +e. H. 20
20 + 2. 20. 21 n + 21 n
19320 + 2. 10 11. 20n + 11. 20 n 
+2. 10. 20 21R + 4. 10 1 2031n + 2. 15 2021N
+ 10. 2 n. + 2. 10 1 25 n + 1i ai H
10. 2021 B 410. 11. 20. 
10t. 25 p2 10. 1125 X
hv = k10 + Ah 183 H1n + 6h 10. W N + 4h 1D. 1pn3 + h W1 n
1(B)
O2 = 30 + 2. 30. 31n + 230. 32 n
+31. _ n + 2.31. 32n + 32. n 7
sit ergo 30 = (202+ e. 10. 20 + h. 10 et 32 = 121 + c. 112. 21 + h. 1, 4
t
et 31 = 16. 20. 21 + 6h. 10.112 + e. 11. 20 + 42. 10. 11. 20. 21 4 6, 10. 21
suprsunt duae aequationes. 2. 30. 31 = 4. 20: 21 + 4 h. 103. 11 + 2C. 10. 11. 28 + 2C. 10. 20. 27 + a h. 10. 11
et 2. 31. 32 =
2. 31. 32 = 4, 20. 21+ 4h. 10. 113 + 28. 111. 30. 2] + 28. 10. 11. 2p 4 4 h. 10. 113
2
et fit 6_ 20+ C. 10 W0 +h1 in 6. 20. 2 +6he1. 1 + C. 1. W0 4 4 p. 19. 1. 20. 21 F e 10. 2
et fit +20 + 2. 10. 10 in 6. 20 2p + P. 1 2 + 40. 1011 20. 2 = (21, 2. 10d  P. 1. 1. 4
2.
+h. 10
6h 18. 15 C. 10: 25
Item sinilter + 21 + e. M. 2, in  . lo. A 1. 
(20)
J2H 10. 1(3 P. 10. 11. 2)
Quae duae aequutines 19 et 2o solae restant praestandae. fit C- fLgA - NN: B.
t h. 11
fit LLB= NNA et quia aliquiod arbitrarii superest, faciamus C = 0 fiet L = b et M-0
ot L= 0 fit 1. 21 = 11. 2h. 10 +  C. 10. 20 4 21. 2. 20 + C. 10.20. seu
(23
11. 21 = -  20. 228 + 2. 18: 10. 2h. 10 + P. 20
et ex N ~0 fit 1P: a 1I: 213. 2h. 10, + 11. 21 e. 20 + 11: 21 C. 10 + 2. 20 =0
ita in aeq. 23 substituendo valorem ex aeq. 22. fiet:
28,2. h 10. . b. 2. 2 4 C 1) +26C. 20. (2) 2. 2 + C. 10. 10. 2h. 10 + 2. 20 4 20. P. 10. 220
2h1c. 28. (] 220+ C18+ C. 20, 20.10 (21228+2.10. 2h. 102+ P. 25. + C 10. 20 10 220 L C10 ) 1. 5. XC 0 pJ. 2 10 (. uv
Rarsi in aeq. 21. seu ob C = 0, fit C 6h. 10: 11: 21 + 4 C. 10. 20 CII. 31 + 6. 200, ubi lollendo 11. 21
()
e. 10
in aq. 25. per aeg. 22. habebitur rurtus aq. inter 10 et 20. Sed video cum aeq. 24 sufficial ad 
e. 2
ere
invenendam 10:20, si iterum reperiretur C. 10: 20 per aeq. 26. prodituram vitorem, inter
eat relationemm inter datas quod non licet. Itaque  jam vide, non licere ad hibere
eqvationem 21, adeoque 1 nec L et M sed simpliciter insistendum esse aequationbi, 19. 20
evera enim res redit ad duas incognitas 11: 2 et 10: 20 sit li. 21 =  , et 10. 20 =
set A- 269 1+ h p + C p et C = 28 2i, 6h p4 + C99 +. pp + de P1N6, et L = 20. 1, 2 + Bt ex qt ep 
ce
et M = 20. 2B, 2YP9+ CG tefq
seu brniloque A = 20  20 D  B= 21E C = 20. 21. F L = 20.  Q M = 20. 213R
a 1+ h 9t + eq
et et cpag 19 (20. 29) DF = (28. 2 2 et (21 20( F = (20. 21 R
derge
epE
(2
1+ eq +h4t, in 6 + 4 epqt Cqq + pp +6pp 9q = L2, 2 + exq. + C q + 2h past
ab qu. 27. subtrahas aeg. 28, fiet c9. (29) divisibilis per  p-9 adeoque licet facere (2) p26
 27. slis equalu 1+ ex + hpt, in 6+6epp +6p ( 2+ + 2hp quae aequatu est
e +ahpt, adeoque fit (3) + 3C pp + 3 p =  + EC p 2h pt
 quae est plana
t = e pP = . sed jam video non licere in gredi hanc viam, nec facere
instantum, unde et xe foret stans contra hypothesin
et 2 essolvre alio modo ordinario nempe per ag. 27 habetur q4, cujus ope
d hhabebit ratiorem
vatio ad solam p quae verect ne satis alte assurgat. Hoc  soluem
velitur cgil t ar. 27. et 20 palte Por q este rad es esisde aequalibus