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# Title: LBr. 705 · Overbeck
# Folio 25r, page id DE-611-HS-861255:0049
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 24v); this page is its right half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 65 lines, status machine
# Lines: 65 recognised, mean confidence 0.93
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

Aliud Exemplum: Quaeratur linea undecima
numerum Lateris,
Resolvo 11. = 8 +2 +1., quae partes metratur 16 per Quotietes, 2. 8. 16.
Ergo colligo Progressiones 0. 1. 0. 1. Iten 0. 1. 2. 3. 4. 5. 6. 7. 0. 1. etc:
_ 3. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1. 12. 13. 14. 15.
16.
Et facto Denominatore comuno 16
pono 8. B, 0. 8, 0. 8. 0, 8. 0. 8. 0. 8. 0. 8. 0. 8
0. 2. 4, 6. 8, 10, 12. 14. 0. 2. 4. 6. 8. 10. 12. 19
3.
1. 2
5. 6.
8. 9. 50. B. 12. 13. 14 15
Suma v. 1. 6. 17. 12. 23. 10. 19. 8. 19. 14. 25. 20. 31. 26, 37
Lineam in pleno systemate Periodi Summativae
Quaeratur Linea Abaci ex Problemate H
Qualis autem Abacus sumi debeat Canon paulo ante Problemal. indicabit
Singula membra Abaci multiplicentur pen quadruplum Numerum Lateri
Si Numerus Columnae desinat in 1. ut 21. 31. qi’ etc:) dt inveta finea bis reponitu
At si Numer: Colu. desinat in 0. ut 10. 26. 30. 40. etci singula membra
Lineae inventae multiplicentur per octuplum Numerum Lateris Abaci e in
venta Linea quater reponetur
ut in Coluna va petitur Linea devigesima secunda. Seu Portio 22.
Z + -1. - 32. tot mebra sunt in Latere Abaci quo indigeo. Ergo 32. Numerus
Laleris paratus est.
Et quia poscitur Lortio 22. resolvo hoc in 16. 4. 2
e dividendo Numerum Lateris 32. per has discerptiones repono Quotietes 2. 6. 16
e sumo Progressiones 1. pro 2.
0. 1. 2. 3. 4. 5. 6. 2. pro 8.
et 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1.
8, 12. 13 14. 15. pro 16.
Sed omnium earum Progressionum Communis Denominator debet esse 32. aquali
perpetuo ipsi Numero Lateris in Abaco cujus Linea quaeritur
Ergo vario Numeratores, ita ut valores quadrent ad Denominatorem. Con
munem 32. d scribo eas Progressiones hac serie
pro Quotiete 2. Progr. 0. 16. 0. 16. 0. 16, 0.16. 8. 16, 9. 16. 0. 16, 9. 15, 0. 16, 0. 16. 0. 16, 0. 16. 0. 16, 0. 16. 0. 16. 0. 16
8  1 0. 4. 8. 12. 16, 20. 24. 28. 8. 4. 8. 12. 16, 20, 24, 28. 8. 4. 8, 12. 16. 20. 2928. 0, 4. 8. 12. 16, 20, 24, 28
16 a  0. 2. 4. 6. 8. 10, 12, 14. 16, 18, 20. 22. 24. 26.28, 30, 0, 2.4, 6. 8, 10, 12. 14,16, 18, 20, 22. 24, 26,29, 24
0. 22. 12. 34. 24. 46. 36. 58. 16. 38. 28. 50. 40. 62. 52. 74, 0. 22. 1234. 2946.36. 58. 16. 38. 28, 50. 40. 62, 52. 79
Sed hoc inventum bis reponendum est
ac (6. 22. 12. 3424. 46., 36. 58. 16. 38. 28. 50, 40. 62. 52. 74. 0. 22. 12. 3424. 46. 16.58.16. 38. 28. 50. 40. 62. 52. 74022.12. 3+ 29 46. 16 58. 16. 38. 285040 b2 52. 74. 02 2 12. 34 24. 46 365816.3 4. 28. 50. qubrpe
Hujus inventae Lineae singula membra oportebit multiplicari per quadruplum Numerum Lateris
seu per 128. et denique singulis (mebris suu eoadratum addi quibus Quadrati
supra spoliavi omnia mebra ut in hac nuditate mebrorum progressionem certive
prehenderem. Sic membro quod ordine est 19 num addi debet Qvadratum
Numeri 19 seu 361. et sic in aliis.
Quae operationes si Actu ipso non ita commode institui possint mihi tamen satis est
primo probasse quod res sit in potertate nostra, ut extra seriem ad quamvis
Columnam possimus exhibere desiverata Portionem in Percodo Summativa
Posteaquam vero probatum est periodos sumativas extra feriem, esse in potestate
etiam probavi quoo ipsa Periodi suet in potestate extra seriem.
Nam
si summativa detrahas summatioa proxime inferiorem, Residuum est
quaesita Periodus sed ne hoc quidem opus est, quia quicquid ab inferioribu
ultra debitum ad superiora additum est, id totum in Fractionibus subsistit ut tam
facile sit distinguere puram Columnam ab additis inferioribus, quam facile est
integra a Fractionibus dignoscere
Exemplo sit supra inventa Colamna zi summata quam sic expresserama
0. 1. 4. 9. 16, 25. 36. 49, 0. 17. 36. 57. 16, 41. 68. 97. 0. 33. 4. 41. 16.57. 36, 81. 0. 49, 36, 89. 16. 73, 68, 129
evaritur hinc Col. 21. e
13C. solitare
per 32. missis Residuis et ex serie Quotorum fiat Periodus Col. 21 solitaria
ut 0. 0. 0. 0,0,0. 1, 1. 0. 0. 1. 1. 0, 1. 2. 3, 0. 1. 0. 1. 0, 1. D. 2. 0. 1. 1. 2. 0, 2. 2. 4
Expurgado, v. 8. 8. 0. 0, 0. 1. L. 0. 0, 1. 1. 0 1. 8. 1. 0. 1. 0. 1. 0. 1. 1. 0. 8. 1. 1, 0. 0. 8. 0. 0
se facile bata periodo summata ernitur vera Percodus.