# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068207:0149
# Permalink to this reading: https://leibnizlegible.com/page/00068207:0149?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 75r, page id 00068207:0149
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 74v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068207&page=149
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000149.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 124 lines, status machine
# Lines: 124 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.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

m. mt m m m m m qu.
2. g. 1. 2. 4 1. 2.
Retid. 1. 3. 2. 6. 4. 5. 1. 3.
4. 2. 1. 4. 2. 1. 4
c4. 6.
Resid. 1. 6. 1. 6 1. 6. 1. 6.
Repd. 1. d. 0. 0. 0. 0. 8. 0
dlesid. 1. 1. 1. 1. 1. 1. 1. 1.
Obsero. 15. Probari id ita potest: Omne
Numeri in Progressione dgadica
a loro m etr: sunt quaterni Ab
his ergo si auferatur Lvaternus
divisor quoties potest non dani
possut allia residua qua Qvaterna
Quatermarius enim metiens totum
et ablatum metietur e reliquum.
sequitur ut consideremus 28 Divisorem in 0Atodica Progressione Alitae enim
Progressiones loco ejus Critico Unitatem non habent
Sed de eitodica Progressione idem dicendum quod observ. 15 octensum
est, nam d hujus Progressionis omnes Numeri sunt evaterni.
Ergo ipsi 28. in nulla Progressione Charaiter primitivi copetit
Examinetur etiam 21.
Hujus locus Criticus est m Sed m: in sola Progressione senaria residua
habet Unitatem. At hujus Progressiones Numeni omnes sunt terni et Divisa
21. etia est terng. Ergo omnia ejus Residua erut terna p Observ. 15
Nutlum ergo Residuum Unitas est. Quare ipsi 2. nullo loco Charater
primitivi competet in hac progressione.
sumatur autem etiam Progresio Oitona quae etiam loco m
Critico habet Unitatem
Divisar. 28
m = g. me m m m mt ec: Haec Progressio locis paribus habet
Unitatem imparibus vero octonarium. Ergo mZ habet 8. Non ergo
ipsi 28. in Pogressione ectona Character primitiri competit
sumatur Divisor 21.
m = 8. n m m m etc: Etia ad hunc
Divisorem loca imparia habent Residuam Unitatem
Ergo ipsi Z1 Divisori loco mro Character primitivi com
petit, etsi 21 sit Numerus Compositus
Quare propositus Character Numeri primi, non
est reciprocabilis itaque valde dubito uttrum hic Chara
Aer id quod quaerimus conficiat nec ne
Possemus quidem excipere illum Casum a novam
legem addere ne sumatur Radix progressionis major
ipso subdivisore.
Sed dum Numerum Z1. examino, suppono me
ignorare utrum 21. ullum subdivisorem admittat
Incertum enim adhuc pono utrum 21 primitivus sit
pec ne. Qvare hoc parto nescio utrium 7 sit subd
visor Diviforis 21. nec ne Quare haec lex frastra eris
data quoniam haec lex supponit me nosse quod
primitivus metiens ipsum 21. ut caveam ne D
sumam.
Specialis tamen Regula formari posset, ut examen
subt suscipiatur in solu Progressione Dgadica, sic enim
nunquam continget ut Radicem Progressionis suman
justo majorem.
constat igitur si ad solam Dgadicam Progressi
onem attendamus posito . primitivo, semper loco
y-1 Refiduum esse Unitatem.
Et hoc posito patet omnem Numerum parem
carere charactere Numeri primitivi per Obsesro. 15
Accedimus ergo porro ad ternos Numeros impares
9. 15. 21. 27. etc:
mo. m= m= m m: m m m = mD in 2 m M M= n2
1.
1.
1.
2.
4.
4.
4.
5.
1.
2.
1.
8. 7.
8. 1. 2. 4. 8. 1. 2. 4. 8. 1.
8. 16. 11. X1
2.
8. 16. 5, 10 20.
4. 8. 16, 1.
22. 5. 10. 20. R
d. 16. 32 19 38. 31. 17. 34. 23. 1.
8. 16. 32. Y. 14. 28. - 1.
8. 16. 32. 1.
2.
13. (26 - -1) -2. -4. - 8. - 16
B 16. (. = 2f : 24. = 8. = 16 + 4. N. 4.
8 16. 32. 25. 11.
8, 16, 32. 13 26.
A.
4. 8. 161 32. 64. 59, 49 29 58. 47. 20
13. 2b. 52. etr
Ad D Subdivisor7
n = 2) Resid.
9 Loco 8 dat 4.
15. loco 14. dat
21. loco 20. dat 4
27. l0co 26. dat 13
33. loco 32. dat 4.
39. loco 38. dat 4
45. loco 44 dat 31.
51. loco 50. dat 4.
1.
esid. 1.
Resid. 1.
63. C0ro 62 dat
ex quibus omnibus parum
certi colligitur.
Divisor 9.
Divisor. 15.
Divisor. 21.
Divisor 27.
Divisor. 37.
Divisor 39.
Divisor 45..
Divisor 51.
Divisor 57.
Divisor 63.
Divisor 69.
57. loco 56. dat 4
4.
8.
1.