Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 86r

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: 0.78.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 85v); this page is its right half.

The machine reads it as

1. lxx + amx taan =0 Uxx talmx + aaln = 0
2. aaemm c cantraque namm aamm- aualu,. A
3. DxX + aaX taaq. =o (Et parijute X - -y + a VCq. ApI, . 2
4. compendio ac =mm-ala aD = qq- apr lq. pm = a5
5. Aequals duobus valoribus ipsius X sit -pm +sa C = - l9 + lYa D et G- pa = l sa D - p aC auss laD. ppaO = Al 2al p 16D
6. a5 au (ppOsC aa lBDF au p DB ( aalpp CD = a aBfit radss CUD App C) = (4a a lpP
7. Ergo sit a (_ ), = ) = a a5 Y (allD + a pp () - a a 55)
8. Zl a D = 99 - elpr
9. Y =ll94 + pum m + 2lmpq - 8lp (lr L. pp)
10. pris
11. 2aC =Eppntu -8Inpp
12. aais = - Uqq - pomim F2mpus d sic l tmmtrtupque - lq hemm remipis lam)
13. fiet lostut d
14. et sist. p aes tisaa _ fic a (ppo + lD) = as Aequ (Iqupm) - Ep (traap )) (19 - pru)
15. ergo quelqu pu)- lp (hens) aqvetur quadrato a (lq +mt rtup) bp
16. et fier d qump) tp Clre p)= qu 4 mp) L X qustranp 2(lqum (lup)
17. et divisis omnibas per trinp fit 2H (t qum Ip eV tr. In)
18. a
19. et fiet fa5 pp C + aslD- U+ g m- etr np)
20. AaO = lgmm Apprum Lapptu L pg Ulqqu + +llpV s ((qu CG. m) - lp (tr + ap))
21. sit (qu (lq +mp Zlp (Ir+np)= (qu et 9+ mp) 1 qu (tremp) 2_ (Igmp (lr tnp)
22. fit tp Clrrp) - 2 (tq tmB) et qpuam +
23. et f ppum L Applu f Ugq f Alpr F, lqemp- V (lrtup)
24. Qrarum binarum opehabetur n et r. pi substituti in aeq. 5d
25. 5 + = g9 ff + h sit _ g= f + hE et fit (A 2hf e + sin et ()+ kh unde h= Naa- 25 a
26. eta sit ft he (4) = 9
27. se f.+ K 2t2 g. ubi pro f, lxg ponatur valores
28. g- ap eg7 alo
29. Exaqu est Ex datis est f = lq +mp K = -Ip h = lr +np haec substituaantur in ae
30. pet lgtmp _ lpa a25 et fint lrtuple
31. paa .-Elqtemp, a
32. et inaque et ex ag. sit 19tmp + (renp) C +m + Appam L Appln +. llgq. f allpr
33. Harum duarum aegus. ope tollendo Y, habebit aequatio quaesita ubi sublata est X
34. et tantum pro Y ponitur eius sulor per ceteras et assumtam e
35. ex ag. 5 ope 6 fint flp a - m (1g2m = (pmm -= l199) + aupY - A pp ln
36. e sit r =Ba pin (ep: e). L 2(1a tap) - (port lus (pan lq),. A Up
37. si + =k-
38. sen appta L (1q. pnif (le + alqump)
39. fiet r2 appla _(lq- pm) l0a = ll9q + mmpp,: allp
40. Hoc valore ipsues r substituto in aeg. 5 habetituraeu vitio ultimm
41. nempe apuln -(lq- passege - l gg + nmpp +. 4 l pup. L. all ppea - (q n) ga lp
42. sed sed e habetur ex Y per a9. 9.
43. Sed calculus esset repetendus
44. ta (erO HD) = fq - pn) f(B quelqrem) quC lq. pn) 8lp (tr+ np))
45. d ququ(tqrpm) quelq pud Almpq. Et fot sint sucdu
46. Exx + max + ndaa pex t gux t raa
47. Fa (op 13 - (19- pm t (lropes L p (mq fr - 1))
48. Fa (pphum-alu) + l (99 - 4pY) = (lg - p m) Y (qu (l9 + p mi) - 8 lp (lrAa p))
49. im - an = a C lg - m = as lg + pum = a t, et fiet B apO tllgq- a pr = as saut. sp (hrinui)
50. aa p( +llqqu vocetur aG, et fint aC - allpr , : a5 = fCaatt - 8lpnp = Bl pY)
51. aaH- 8 Ipup vocetur a2 et firt aG.alpr: as = + (2 2 - 8lpr)
52. sit a -Elpr = sint pr Z a2 - aa ee,: 8l, fat
53. fint a3 Ex aeg. 1 fit ag -alpr = aa se, ubi pro por su substituendo valorem
54. fit ea-(a2 - aaec) = aase se 2aG + ec = a7 + se
55. posito ( = ap (mm -alui) + 1199 442
56. A et 2 - (lgemp) - 8lupp e a5 = l9.- pm e = s (au (liemp) - 8 lupp 8l pY)
57. aa p a pau 3O + aa l DD + OD = 55HL aa Bassi - 8lp5 5 ad = p BB , (EDB F 2ppllOD
58. ad = lranp
59. 1i M, n, P, 4.5 sunt datae ad = mm ala aD = 49- + pr as = lg -pm At = lgemp Cq mp
60. conservo Y
61. Ertup=ad

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 86r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068207:0171?run=74