# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068041:0028
# Permalink to this reading: https://leibnizlegible.com/page/00068041:0028?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 23
# Folio 14v, page id 00068041:0028
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068041&page=28
# Source image: https://digitale-sammlungen.gwlb.de/content/00068041/jpgs/default/00000028.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 32 lines, status machine
# Lines: 32 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.
# 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.

Mati 1678
aer recipientis majoris a
a
per inde defractus b residuus in majore a = b. inde rursus detrahetur
unde detrehendus
a
qui sit ad residuum, Y, et B ad _ = aequ. =. Ergo d aequ. = Y. et sequens residuum (Y). est
r- d.
ent:
C
a
Erge (Y) aequ: Y- =Y, seu (Y) aequ. a a - b Y
a
Hinc serdes resicluorum
a. a- b a-b a b estc. sunt ergo progressionis cxomesiicae.
Ninci
si ceres residui sint ut numeri, erunt a exhaustionum e multitudines ut Logarithum
oidendum autemaq possit dere progatos quovis numero qui progressionis geomehricis non sit possit definiv
uc undo Logaritoma. Nempe si maeter tres exhaustiones subjiciatur ladhuc una dimidia extractio. Sed lea ut
video rem non efficit. Interim hoc methodo illud efficietur purcherrimum, ut possit excotar. potentia
altistima, vel extahi tadix cujus pura cuduscanus gradu solo extracstionum vel ad missiorum aeris certo numro
xg
aligi Aruo video sic solum procedere tantum excitationem potentiae seu multiplic
trobem non vero exfractionem, quia a et b. adeoque et ab. jam dantur adeoque finstra plr
ex
si
mero
 poe sine avalde magna, b viede parvu v.9 rix 100000a pribris, quod facile est
spatiorum folidorum proportionem trilicetam et adhibeamus instesuttum intus tubata montrutem aeris quantitate
accedu se indice mnisis exactitudini causas et conversionibus emboli instiam ento dentaso se nporantsu mulcherame
ex ractionem quauntur.
otatuos sn calclo invenenus cavendum de abris mntatio mocent