Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 103v

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.77.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 102r); this page is its left half.

The machine reads it as

1. yy + ab
2. si possia tatid facere ratonalem habebo dimensionem curvae Hyperbolae. Nam si y-aaix
3. tiet Paxdx 1 dus ay = lat x dx. xx Habeo et meisionem ipsius TarX x seu dimensionem
4. curvae parabolae cubicae. Nam si y = x. zua fint dy = xX p: na et fiet Suidus+ avax- var xiea
5. utraque enim summa iniri pt rationaliter, quod patet. Nam si sit S+X= y seu si fit
6. X. = aagy - ab seu x = Ilaagus - a b) tique pat unde si X habetur intionaliter datur summati
7. Mursus si sit Oaa b +x _: XF - y. seu yy X = aeb aa X seu X N = a b: yy-aa
8. qp
9. +rmm hpbens
10. ita rursus lantum opus est redd Dguaa fieri rationalem.
11. mo auplius videndum an hon hoc reperto omnis curva Conicasi
12. summam rationalem, Nempe sit sitaq = Z2+ aC+ aecio et A aagus adebet fieri
13. aequalis ipsi Z et fiel (Z + rac ZZ + 2 a 77. V + aa ee + 2ae: v + acc. vo a2 (8
14. 2aC 2 VV = 2ac82 + aa cevv ab + 2ac0Dt at seu-
15. +a sit ee ab et fiet 37 - 24 aceV, a cc
16. tanec vo + 24e cev + acc
17. rahonalifatione ipsius Saagus a b. Hinc etiam datur (gaZ. ergo datur Z2dq + aedque + (a c. V) dz
18. sit at. co ergo dater codque
19. Eagos datur et Zduo
20. Z7 = 2ae + CCCOC:, 2aC + 2CC0 Ergo datur (d(raceCor cccoCO,, act 0)7
21. Nempe sit ay = 23 + av + ae firt argy - a b = (Z) +2)ZV + 2 aCZZ + ecvv + racev + an ée - ab = (2
22. 22=ca0v +: 20+ 2ae
23. quia autem datur szclus ex posita
24. rationalisatione ipsius aagus- aeb ergo dabitur et sydz. Ergo et S22dZ + Sevaque + Saedz. Ergo
25. videamus jam an omnis curva condea ad formam
26. mXX+ ad: nXX + a ,odx summari debet sit X7 = 50 et 2∞ dx = F du
27. Ergo et Sz d
28. catuur et sodZue
29. seu ax = fdb: 2YV, fiet summand. ergo Sin f∞ +a;, nsv + a, fdv: 21f0. se
30. ipsius reduci possit
31. Jinfo +a 5fov + afV n fav: 2 si pro s0 scubatur aas.v pro do fiet: - acc: vV
32. et habebimus s infaa: v +a,: ns at v + af. B faa dv: vo. seu fiet
33. Generalius sit XX = asv Yaag,: v fiet 2Xdx = -agdv:p
34. seu dx = - gdv: v0): 2 NB:, 5ur a) ex et ex Y (mXX+ a) : (nXX + 2)) ax fit:
35. mo = max + in A3 + a
36. anfv ratrusa matix
37. sit K
38. et ams
39. amabus
40. N = m in a XX + a = aagu dat _ a0 p m XX + n r a ausus a - m
41. seu XX +. 2 men a = s-
42. aneti
43. na hun
44. C+x B+ D. = CC+ Vp + 2B)
45. s Bβ = .. . .. VVEr() -. nen
46. β= .
47. est autem is rationalis ex Hypolhesi = 8 tinc VV + 29γ - da V~ F 3+ 2 - du. 7
48. Ergo fit pV+2 Y, V = l
49. et et
50. yrb= mx gob = ep fiet sgs bb -mnpi aa et m pato = npaab seu p idela;
51. et fint yy- b0 =
52. mm - nn
53. agerentis istetqu
54. mup- amno, hujus quaeditur sit amnp + axq quadratus
55. um np
56. nonel sala
57. Ergopo
58. ammpranmu ratun aegum - aequn = oto sit am. n = W fint 2a + aquoro- aq aus
59. a a o-aa eali mx
60. 7 +b,n P. ad ytc rp: aa Ygeb, stC= map: aa g = ump = gab, aa = n
61. sit p aub a
62. un uocabo as pu heosbit Cmmanu). veit
63. yrbb minim r i
64. E ac v0 +2c
65. seu datur quiaantem datur sytus - (d. gu. lb summat erd rationali ex posita
66. 2evn+ racv
67. ah: co, fint 2Z- Ena race. co 4 adcl:, rea. co 1 cico, seu fic t
68. adeoue hutur et (a C: D) Azue
69. et. 23- et
70. dofall sinsvt avv: n + asv
71. 0d
72. ioast Z 6
73. sdaa. Erge
74. Vhrtae
75. eltis

Cite

Leibniz-Handschriften zur Mathematik LH 35, 8, 30, fol. 103v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068124:0206?run=73