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Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 210r

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: 0.87.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 209v); this page is its right half.

The machine reads it as

  1. nica: Sciendum est, muleas series numero terminorum infinitas, esse in
  2. summa gracitates Anicas. Exempli Facillimiloco sic series ab unicate de-
  3. crelcens, progcestionis geometrica dupla, L,f. Z, f. 5 rt. 2o L5 L. For c
  4. in intinicum; qua camen non Facic plus quam 1. Nam in adjecta
  5. linea recta AB (FiC. 4.) qVX SICL, CTIE ACL, e residuum (CB) bise-
  6. cando in D, habebis CD Z; de residuum (DB) bisecando in F, habebis
  7. DE, 8; de residuum (F B) bisecando in F, habebis FF, 7G: d ita
  8. concinuando sine finc, nunqram exredieris cerminum B. Idem in
  9. Fractionibus numerorum fixuratorum scu crianoulo Fharmonico fcri,
  10. a me alibi octentum est.
  11. Mulca nocari possene circa hanc Oradraturam, sed quae nunc
  12. PErseqri nOn VaCAL: hOC LaMeN PraeterirE NOn OpOrTCC, cerminos se
  13. riei nostrae, 2, F, Z, 3 Z _c, esse proorestionis harmonica, sire in con-
  14. tinua propoctione harmonica, uc experienei pacebic: Orin e per
  15. Calcum, F,5, 5. 5, E7 dc, elt etiam series progrestionisharmonica;
  16. e ∞ r9d est icidem series harmonice proporcionalium.
  17. Ttag; cum Circulus (IcZ F. X F5F L, _cc, 5 4 itr 15 od
  18. Polteriorem seriem parciale à priori Cuberahendo; cric magnicudo
  19. Circuli differentia duarum serierum progrectionis harmonica. FC
  20. gronam groccungre cerminorum numero finitorum progrestionis
  21. harmonicae Cumma, compendio aligro iniri porest, hinc approvin-
  22. qraciones compendiolae, (Ei post Ludophinam illis esset opus) duci
  23. Pollem.
  24. Si quis in serie nostra cerminos signo n affectos collere volet,
  25. is duos proximosi F, ilem (.Z i item 1( B Y. dCrt +5 5 d
  26. te 19, ee ita porro, in unum addendo, habebit seriem noram
  27. pro maenicudine Circuli, nempe Z ( id eAt f. 5) f (id est = Y
  28. 490(lC8 .) dec. itaquc:
  29. Quadrato inseripeo existente.
  30. Eric Area Circuli 5F55l59Fr 95F325 ec.
  31. Sune autem numeri 3. 35. 99. 195. 323 ec, excerpri per Caltum ex
  32. Cerie numerorum gradratoru (4. 9. 16. 25 dcc.) unitace minuIOruM,
  33. unde hc Ceries: 3, 8. 15, 24. 35. 45. 63. 80. 99, 120. 143, 168. 195. 224. 255.
  34. 288. 323, 360. 299 ec; ex cujus seriei numeris, quartus quisgre post
  35. primum noster est. Inveni sutem (qrod memorabile est) leriei in-
  36. tnica 5F5 F∞5 L25 F 55 L FL ZL05 F0c. summan esse J: quin
  37. X lira-

Cite

Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 210r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 44). https://leibnizlegible.com/page/00067993:0421?run=44