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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 27
# Folio 2v, page id 00068240:0004
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 1r); this page is its left half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 124 lines, status machine
# Lines: 124 recognised, mean confidence 0.85
# 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.

. 1. 2. 3. 4. 5 6. 7. 8. 9
posito bra fit: 11d+ 2F 24d
er tecda esile) o.
2+ 3. ponita jam 4, quoque f7 1
posito divsore 1 fit:
nempe residui erunt : 1. 0. 1, 0. 1. 0. 1. 0 etc.
s 8. 1. 0. 1. 0. 1. 0 ese multipheati per 1. seeurs
per 3. dant residuos: 0. 1. 2. 0. 1. 2, 0. 1. 2. 0. etc., per 4 dant 0 2. 2. 3. etc.
Multiplicati per 2, sunt. 0 2. 4. 6. 610. 12. 14. 16. 18. 20., divisi per 1, dant 000 per 2, dant 0,0. 0. per 3, dant. 4 2+
0. 2. 1. 0. d. per 4 dart, 0. 2. 4. 2. 0, 2. 0. per 5 dant 0. 2, 4. 1. 3. per 6, dant 0. 2. 4.0. 2. 4 d et per 2d
per 8 dart.. 0. 2. 4. 6. 0 per 9: dant. 0. 2. 4. 6. 8. 1. 3. 5. 7, per 10 dant 6. 1. 2. 4. 6. 8.
Multiplicati per 3. sunt: 0. 3. 6. 9. 12. 15. 18. 21. 24. 27. 30. qui divisi per 1 dant residuos: 0-0- 0.
per 4 dant: 0. 3. 2. 1. 9. per 5 deliaquant: 0. 3. 1. 4, 2. 0
per 7. dant 0. 2. 4. 6. 1. 3. 5.
per , dant relinquunt: 0. 3. _ 3. 0. etc.. per 7. relinpoint: 0. 3. 6. 2. 5, 1. 4. d. per 8. velingmut: 8. 3, 6, 1. 4. 7. 2. 5. 0
per 2, relinquunt 0, 1. 0. 1. 0. 1. 0. etc. per 3, dant.. 0. 0.
et 10 relinquunt: 0. 3. 6. 9. 2. 5. 8. 1. 4. 7. 0 per 11, retinquunt 0. 3. 6. 9. 1. 4. 3. 10, 2. 5, 8. 0
Multiu ocati per 4 dart: 0. 4. 8. 12. 16. 20. 24, 28. 32. 36. 40, qui diusi per 1 dant 0. d et
per 2. dant 3. 0. per 3 dent rclinquand 0. 1. 2. 0. per 4   70 3t per 5. relirqouit 0. 4. 3. 2. 10. per 6, rel. 4. 2. 0, per 7 rel.
9 relinysunt: 0. 3, 6. 0. 1
4. 1. 5. = 26. 30. per 8. rel. 10, 4. 0. etc. per 9. rel. 0. 4. 8. 3. 7. 26.1. 5. 0 - per 10., n: 0. 4. 8. 12. 6. 0.
Multipl. per 5,  dant, 0. G. 10. 15. 20. 25. 30 35. 40, 45. 50
et it veltiquiit: 0. 3. 6. 9. 0
dividper. 1 rel. 0. per 2 relinge. 0. 5. I.   per 3, rel s. 10. a 0. 5. l. 0. per 4, vel. 8. D.  3 3. per 5, 6. 1. 9. per d vel. 5. 4. 3. 2. 1. 8
rel 
per 11 rel. v. 4. 8. 15.9. 2. 6. 10 3.70 per 12., vel p. 4. 8. 0.
0. 5. 3.1 - 642- 0. per 8, rel. 0. 5. 2. 7. 4. 1. 6. 3. 0 Per 9. rel. 9. 5. -1. .  8t.  fh 10;
per 11 rel. 0. 5. 10. 4. 9. 3 82.31. 6.. per 12. ccl. 0. 5. 10. 3. 816.  4, 9. 2. 7. 0. pr 1, 23. 520. 2. 7. 1. 4. 9. 1. 6. 1 5. 80
per 7. de rcl.
Aegula ergo Gegeralis
p resis aterum et terum
isit. sed quando id a quo sutrohendum est, subtahendo minus esst, diferentia inter divisorem est,
Y Numri natuciles, muultiplicati per 1. addito 1 F
quam inde duco haec est: prim asiuorum sub tra hitur a des
primm pesiduum ep diffentia in sublucta a quolibet Residuo relinquit sequentem residuum nodo sa quo subtrahendum est,
subtratendu minor est, divisore augeatur. Ita 13 C H 8 5  pe 14.. rel. 0. 5 10. 1. 611. 2. - . 123. 8. 13. 4. 9
etque ita continue honec uiste
Regulam ergo generatem hanc observo
in sege multiplorum, pltinum duorsore minorem, ab eo, tubtrahe, residuum a primo subtractum, dabit primum ortiorum a secundo nattio
0. 5. 10. 0.
v. 5 10, 15. 4. 9. 14. 3. 8 3. 2. P 12. 1. 6, 11
data subtrahendo minorem, divisore augendum esse. Igitur omnsum
acundum ortivorum et ita porro, modo nolerur ortronatiosioos residuot, sed et habeas factitios, anxortrvos dixisore ei poductum
diide per differentiam inter divisorem et minimum ortivurus, residuacrunt quaesa fuctitii deruceps.
brevius omnes multiplos divisore minores, auge ipso, dant
pmo, residuus additus primo, et penultimus additus Do, et antexenultimus tertio, etc. dant diisorem
uod si ergo Multplum ilum mnon dati quaerunus qui per dotum divisus relin quar datum. Sic agendum est; ante omnia vide an
ste int qui its, ad est
id est quaere duoru
relinguat 0. seu quaero
quaere numerum natira tem, qui
odictue u duitoris dabit sumer
quod si is o non arte verit, alio est, quam communis omnetiplus (non est aliu quam
produlcat altrum datum
nrabobis, dividendo numerm datum per divisores altius cati
minora est possibilium
iduo s tet
dinicurum Residuorum aptorum
0, statim enim apparet
incipienda a maximis.
pulloma est possibile in ommibus imcica
et videtur possibilis in iis tantum
quod si duo numeri sint primi inter
numerus minor unitate
ca lcutado facile
a angendi proponuntur
esidmum si epe
diviti per 1 el. 8. 0. per 2
minoribus dato; sier nunque tunc longe
 idem, qui duos datos divisorem et
onis u, cui hasono
ops unde jam proporito retituo aliquo sic agemus
suuisorem et sume refidumtus;
hoc Residio eodem modo; incides tandem in uul
ns repete quosu hoc dcendum ex qrisitius complectetaur, injus scilicet Mulape
P. 2. 3. 4. 5. 0.  vel. 2. 9. 1. A. per 4 2. 3.0
4. 5. 6. 5. 8. 9. 10. 1. 12. 13. divisi per 1. relinysbunt. 9. 0. per 2 2etinpunt: 1. 0. per 2
2. rlinquunt. 0. 1.0. per
at 13. 15 17. 19. 21 diviti per
3. 4. 0. 1. 2. M   1. 3.5. 7.
men cum atesset angmentam
et summae per divitorem datu
multiplicentur per E
t li
6.78. 9.10. 11 divisi per 1. relinquunt 0. 0. 0. exc. divisi per 2. relinquind 10. 1. 0. sse X
locum monies.
oi d tant
li 2. dant. 24. 6. 810 1214. 6. 18. 20. 2
tantum augmentum eti
dividatur per B. residuaque ordine scribantur
ducto addatur, 9. sum ioc primum appare
si decedatur per 12, 
iduum 14 sit multiplus
es seroentur
sp renoglads
criors detendum est exerplobes
semper autem ultii  42 - 6
Nunc enim divisor est ipsemed est multiplus quaesitus. deinde a divicori residudatum aufer
Rrasionus datus, sit inter ipsus multiples; si non ita quere illam ex multiplis minimum
 metiuntur ide 3.
a divisre, si asiluus est multiplus tunc
merumus itorem uni
qui ex ipsis fuctia
multiplicandum
x
sie frunt residui:
f. 2. 3. 49. 1. pr b. H. 3. 0. 1. 2
Multiflicati per 21 _ 2. 4. 6. 1. 18. 12. 16
unt ergo sident qui supra
ili 3. rel. 1. 8.  per 4. F rel. 1. 3i  reling. 0. 0. 0
multiplorum etiam
is igisi Numeri naturale
jurdisferenti
lesin an  VLlti
requiritur, minod q
es siciles per p erp. 13. b 15.
c’unde res sie sals fecile perficitur tentan
tempim litib. a
Verit quaesitus: mimorum ioc
post  + Be  a quacudus
=1C, n aise exp
 sed   Adtiaras. S. 2
qu ntlgtus er datum, alti
t ese au t tam s. a