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# Piece: https://leibnizlegible.com/api/records/30067/text
# Catalogue record: 30067 — [Math. Aufz.]
# Incipit: log [...] Videndum an dato Logarithmo Numeri,
# Date: 1703
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=30067&katnr=39237
# Work: https://leibnizlegible.com/work/00068261
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 11
# Folios: Bl. 11r (from the shelfmark LH 35, 3 B 11 Bl. 11r° (=39238)): 1 page, canvas 21, page ids 00068261:0021 to 00068261:0021
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068261&page=21
# Lines: 117 recognised on 1 of 1 pages, mean confidence 0.75
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 11r — 00068261:0021
# Source image: https://digitale-sammlungen.gwlb.de/content/00068261/jpgs/default/00000021.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 117 lines, status machine
c
a
e
a
a
4
L
q 8
2
6C
d
 2-2 = Pxa
2 - 1 = 4X qe
posito e esse impare
Erpo C- 1 est par f.  X t - 1 = X + X + 1, X = 1
Ergo ∞-t
qe- L
-1 = E, - 1 = 2t +1, 2 -1
Nota cua divisor est par non redit
quia numeroum propessionis Geometrici in innfinitum ultimae, notae sunt 2, 4, 8, 6; 2 4 8, 6 Etc. Hinc proposito
pae
ne et thribatur plu Et quia periodus altimirum nomanes sm X 2=L et quia numem
1lid 6 est 4 dicuidatur , 6 per 1, resit  2 2gtat 2 Ergu ultium act est adqu in periodo seu Ca; est uttina
restat 3, ultiua nota ipsius numeri
Ergo 7 est primitivus
similiter
1
lequis
sed omneus tedminatus per 3 divisibilis est per 3, nempe 63
varitur an 103 sit primitivus Z602 quaritur quam habesit ultimam
nolam
A103 per 4 restat 3, ergo allima nota est tertia
in
periodi, nempl8, ergo ipsum 1o2
ultima notu  est Z pergo ed deet dari
9 numerus termineus + F4 per 2, divisibilis per
 103, si 103 s primitivus, quidatur nam
39. 27. 3  3 vice 9 st 27.
10d
quod s jam Gexaminemus  hoc non tantum in progressiore qui
pendica sed e in aliis
2048 4096
log 2 = (e - 1) log. 2
de
128
256
d
16 82
2
 10
512 1024
videndum an dato Logarithino Numeri, quem ob
multitudinem notarum exhibere difficili est saltem
possi
veniri ultimae ejus notae quot opus est, ut tentar possit divisitilius per numeum quendom propositum
notam propesionis duprie
ausi
Re 2
fundamentale
= e. 2R2
-1
 = qX + Y
e
s 2 = gX + r
2e+
+f
+ 2X int +)
2 = 29X + 2Y = (9IX + ∞ EY = (9)X + (Y)
et1
= 29X + ~Y = QX + R, fiet
es 2 = = R _(2. B ~)
e (R2) = E 21
2= 259+ et  R = B = s (2F Y,
int.
A
X
quaritur B (MN) G +Y npe sit nn = qXAr m = Cx + X n = KX + 8 nn= cAXX+ EYX +
qu
+LeX
s n- 5
in casu periodi.
+
sito R M LY 
)  (B2. R2C) = R2. Erg
hic in laso prtodi A ~  si periodus sit f
ergo in casu periodi oportet numtrum f esse  (magnitudinem periodi) esse lalem, ut si nonerm quemunuque inter residios. mudi plices per R2
(o
Ergo RC (nn) = E (XS
ve
quia periodus semper redit ad aliquem numer progressionis Geom. duplae,
etsi non semper ad unitatem, hinc, quaeratu.
0
datae numeno X, quaeritur numerus progressionis Geometricae duplae
qui multiplicans, numem progrigeom. duplae datox minore
relinqua panduant refid divisionis ab X, aquale
producat numerum cujus residurae sit ab X sit idem pa
qui residuns ipsius N ab X
1
Xx- = GXX + R
29X+ Y 2
et = qx + Y 
X= 2
2 qx + 20
R
1a P,:9 Xx = 2
+rY - 2 1
Dx + 1
AX- 1
4= 2
5
M+
6
2
Theorema
C
moducti
in