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# Title: LBr. 705 · Overbeck
# Folio 31r, page id DE-611-HS-861255:0061
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-861255&page=61
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000061.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 195 lines, status machine
# Lines: 195 recognised, mean confidence 0.82
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line: the recognised lines in reading order, one per line.

malia Bimon Trimalia Quine dino
Belus A Cod. 3. Cyclus +
Cyclus _ Cyclib.
ei 119. 1. 1 9. 1. 1
13. 9. alt7 29 2e5. 1. 1.1g 25. qu i l. H. 49. 35. 25. 5y 1
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15. 25, 23, 1, 1. 17, 25, 29. 31. 32.16. 8
1. 19. 31. 28.4. 19. 25. 13
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1. 23. 9. 19 7. 4. 1. p. 29. 18. 2. 3, 36. 16. 13
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17. 41 7 1. 1. 47. 25.5
1. 23,9, 23. 181I. 1.
l. 0. 1 l0 1. 0. 1. 2. 3. a. 6989 39
1. 9. 25 1. 1. 16. 25, 4. 31. 1. 16,25.
1. 17. 9. 13, 25.5. 1.
31. 4. 25. 16. 1. 31. 9. 25.18
1. 32. 1. 32. 1. 35. 1. 32. 1. 32. 1.
17. 2p 29. 9. . 5. g1 37. 3. i
1. 43. 1. 43. 1. 43. 1. 43. 1. 43. 1
49. 13. 25. 4337,. 51. 31. 11
1. 19. 31. 61. 37. 43, 25, B.4
 i es sce re 
10. S 22. 37. 25. 19. 16. 34 4. 28.
1. 17. 16, 3822, 23, 1 17. 16.38.2,23.
. 19. 10. 34, 22, 2825. 7, 16,31. 4. 37. 1
1.29 3. i. 16. 25. 1. 29. 22. 14 16. 35.
4. 25.31. 1. 34, 29. 31. 1,34. 25
37. 4. 31. 16. 7. 25, 28 22.2
1. 3l. 25. 42. 1. 31. 25. 47. 1. 31. 25. G7. 1
37. 25 45, 292, 17 4.t
5 Ey. 27 9. 3. 1. 35.
25. 3i. q9. 3p1. 181. 1. 2.
7. 41. 49 65. 31. 29. 25.
13. 29. 25. d. 2n. 5. quabia
.er. 25. 71. 1. a. 25. 312 ia7 a5. 3I. 1
65. 25. 31. 19. 29. 1. 1. 5u 2. F1. . Fi. 1. 81. i. St. J. Zi
P. 37. E5. 25. 53 410 t
53. 37 qu aq. 3 3l. 59 15.
1. 59. 49 53. 25. 23. 37. 5. 31. 47.1
1. 61. 25. 7. 31. 43, 49. 1937. 13.
1.65 1. 65- 1 65. 1. 65. 1. 65. 1.
d. S. B aii 41. 8. 25
2. 63. 8. 48. 25. 55. 49
.23, 1. 23, 1- 23, 1. 23, 1. 2
 i 129. a. b. 2. 21. 8. du g. 8i
4a 1ob. 19 54 1. 1.35.8.
.19 13. 2. p281. 5, 9. 691
59. 16. 62. 4. 47.1, 1. 51. 47. 35. 25. 43. 81. 83, 9. 19. 1
1.62. 1. 62 1. 6r. 1
16. J. Trub. 1. Tius
1.31. 25. 34. 1. 31. 2
1. 17. 31. 29. 9. 15 15
1. 69, 49, 45. 9. 37. 25, 5. 1
V5. 2i. 67 81. 27. 3. 9. 1.
63. 9. 39. 81. 87, 25. 79. 49. 7. 1.
1.65. 1. 65. 1. 65. 1. 65. l. 65. 1-
1.67. 1. 67. 1. 67, 1. 67. 1. 67, 10
69. 9. 5. 81. 45. 25. 53. 49. 37. 1.
1.13. 49. 5i 25. 65. 81. 1r. 3. pi. 1
1.75. 81. 3. 49. 67, 9. 59. 25. 27. 1.
1. 79. 81. 63. 49. 87. 9. 7. 25. 3). 1.
81. 49. 9. 25. 1. 81. 49, 9. 25. 1.
f. 9. 43. 49. 19. 81. 3. 1
85. G. 61. 81. 21. 25. 13, 49. 39.
.5. 6. 7. 8.9. 10. 11, 12
32. 6463 61.574993. 1
14 4261.5824 9y
 b 3l. 16. ab si aie
1. 16. 61. 2 16. bi. 1. 16. 61 1. 16. 31. 
1. E2. 29 5h. b1. 42. 1. qd. 6. 27
12. 16 43. 14. 6261- 38. 2). 17.
134. A 2. si 3
1. 33. 49. 57. 61. 63. 64. 32. 16
1 51. 51. i6. 16.
1. 2 29. 2. 6i. 23 ig 17 16. 8 9. 6. 1
S1. 6. 16. 21. 5. 91.
i ubo rius 27. 61 23. 1g 22. 16. 55. 9 qu.
1. 49. 61. 6+ 16.4
1: d. . 84. 5. 4. 1
53. 14. 27. 1. 53. 14. 27
1. 5q. 56. sq 16. 19 51. 29   9 6159
Locus
1b. si aiii 3 5.b. Bat
1a37. l. gi. Cyd.15
1. 3. 9. 6. 4. 103. 2
9. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10, 1. 17
. 4. 3. 12. 9. 10. 1. 9. 3. 12. 9
Jo,rO1.1, 01.1 01 1 01.1
. 18. 5. 9. 21. 12 16. 33. 
.8. 12. 5. 1. 8. 12. 5. 1. 8. 12.
910 lto 9,. 12. 3. 4. 1. 10. 9. ii
l. 1hl. i. 1. F2. 1. 12. 1. H2. 1. p2. 1.
1. 3. 5. 13. 3. 21. 15. 17 919. 1.
.5.9. 3, 1. 15. 5. 9. 3
1. 17. 3. 7. 9. 21. 5. 19. 15. 13.
1 2 24.89 3
Invenire Residui Cyelici Supplementus
23. 31. 9. 11. 25. 19. 3. 21. 27. 15.
Ad Cyctum 13. quaero Supelementu Retidui 6. Facit,
nam ipsi dato 6. ad Cyclu totum desunty
Est ergo supplementum quod proposito Residuo deest ad Ey
Invenitur Subtractione
Probl. II. Javenire Lineam dati Numeri Cyclum datio
Sit Cyclus 13. Quaro Linea Numeri
EHaec Linea est 1. 7. 10. 5, 9. 11. 12. 6. 3. 8. 4. 2. 1
Numeri dati 7. Qvadratum est 49. sed cycloter deto
est Retiduum 10. Hoc Residuum multiplico ampla
per Numeru Linece. 7. Fac. 70. Et cyclo 13. quinqu
es ademto fit Residuum 5. Ita jam habemu
initium Lineae 1. 7. 10. 5. Relequa eodem modo qui
Lorellar S. ergo idem Residuu in eadem Linea recurme
1. 21. 2. 21. 1. 21. 1. E1. 1. 21. 1. 1. 1. 17. f1. 3. 7. 25. 15. 9. 2. 9. 19. 1. L C recurreat quoque Residua sequentia, nam eodem moda
 Miladih. sebgil sc.at
l. 19. 19.l.H.B 17 43.317
ex praecedenti Residuo utrobique sequens calculatur
Corllar. 2. Hfinc in omni Linea dantur Residuorum
Periodi, vel ab ipso initio, vel a quovis tormino aliu
P3iig 1. 1. 25. 1. 25. 1. 25, 1. 2.5, 1. 25. 1. 25. 1. Corellar. 3. S Residuum 1. recurrat, Periovus ab ipso
initio redibit, suntque omnes Numeri locorum ub
possut
per Numerum Loci ubi Refiducum1. Primo decur
ra
ob aequalitatem seu identitate Perrodorum
Invenire Residui Cyclici Condrutorem
Sit Cyclus 39. Queritur Condrutor ipsiu 10
Facit 37. Nam Linea 19 e Linea 37. es
una alterius Retrograda atque talium Linea
rum Numeros vocate liceat Coadputores
Habent Condjutores aliam insignem proppi etatem per
quam inveniuntur scilicet: Duorum Condjuturuum
Productum, demtb Cydo toto quoties potest, est
Ut Sit Cyclos 39. Quaeritur Coadpator ipsius1
Id est 19X = 39y + 1. Jam Methodo Ttantoner
domtis per 19 Condivisibilibus restat y +1 dio
sibile quoque per 19. Ergo y - 18
1. 1. 1. 36. 1. 38. li 20: 1. 36. 1s 8. 1. 19 493 (37 Ergo Condiutor - 37 Facit X 37
39y +1 = 703 =19X
Exemplum 2. Qureritur Coadjutor ad 1
scilicet X. in Cyelo 5Z
Pono 19X = 52y +1. Subtrahe 38y per 19d u
Restat 147 +1 =19Z (nam 14 +, quoque est
Ergo 5Z -1 est per 14 divis. (. ber 19 divisibit
sit 5= -1 = 14. N Ablabis  5 divisibilis
restat AW L1 divisibile per 5
e 14 =57 -1. Fac. Z= 3
Ergo 19Z = 57 = 14y +1. Fac. y =4
11 Ergo 52y + 1 = 209 = 19X
Fac. X = 11. Coudjutor quaesitus
Corouar. 1. Condjutorum Supplementa sunt quoque
inter se Coadjutotes
Corollar. 2. Si Numerus Linece sit Cyclo toti con
divisibilis, Coadgutor inveniri nequit
Nam Condivisibile quocuque numero multipe
calum manet condivisibile (Eyclototi) nec absa
to Cyclo toto quities licet Residuum 1. dabit
Probl. VV. Residuum Cyclicum peraliud Resi
Couum ejurdem Linece dividere
In Egolo 65 sit Linea septima inque ea
Residuum 47. dividendum per 37. ejgde Linea
Est ergo 47= 65X =y. Lvaero y in inter
Facit 47+65X, = 37y. Jam Methodo Htan3
noverana ablatis x per 37 divisibilibus fit
47 +28X quoque per 37. divisibile.
Sit ergo 47+ 28X = 37Z Ablatis per 28
divisibilibus restat 9Z - 47 = 281t
1. 29 56. 14. 16. 59. 5i. 54. 61. 39. 3b. 19. 1. ablatis per9 divisibilibus fit W + 47. P9ae
14. 53. 1. sibile Ergo W - 7. ut WV + 47 sit 54 per G divrsibi
Ergo 28)V = 196 = 97 - 47 Ergo 243=9
Sq. 33. 16. 49. 462 1. 3, Facit 2 27 e 37Z = 999 = 47+287
1. 55. ag. 17. 61. 18. d4- 1. 10. 10
l.6l. 16, 44. 61. 24 51. 19. 16. 35. 6.54
27(34 Ergo 952 = 28X Fac. X = 34
Tandem 65X = 2210
228y 161. Ergo 65x +47 = 2257 =37y
38. 16, 17. 14. 23. 6i. 12. 29, 43. 1
57. 16. 37, 64. 2. 61. 8. 49. 32.
 isiticriia
N. Si Residua ejusdem Linerese matuo
dividant, Quosus quoque fit ejuedem Lin
Hinc datis Residuis duorum Locorum
datur quoque Residuum ad eum Locum
qui est arborum Locorum differetia
Sed illud nondum solvi potert.
Datis diobus Residuis ejuedem
Linere videre quanto inter
vallo ea a se invicem distent
qu
.10y. ab. 82
IB. 19. 17.
3. linis. 1
lBy. 1. d7. 1. 87. l. 8p. 1. 8(. 1.