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# Piece: https://leibnizlegible.com/api/records/18501/text
# Catalogue record: 18501 — [Math. Unters., Überschr.]: Proposuit Dn. Consiliarius Schmid 1700.
# Incipit: Data summa numerorum (integros semper intelligo) inter duos ectremos i
# Date: 1700
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=18501&katnr=40798
# Work: https://leibnizlegible.com/work/00068124
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folios: Bl. 9 (from the shelfmark LH 35, 8, 30 Bl. 9): 2 pages, canvases 17–18, page ids 00068124:0017 to 00068124:0018
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=17
# Lines: 103 recognised on 2 of 2 pages, mean confidence 0.83
# 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 9r — 00068124:0017
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000017.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 54 lines, status machine
proposult du. Consiliardus
700
Vata disserentia duorum Numerorum
Quadratorum, data summa numerorum inter
latera interceptorum indenire Nunieos
Vata summa numerorum (integros semper intemu
e
intelligo) inter duos extremos interceptorum,
dataque differentia quadratorum ab extremis,
invenire extremos. sint numeri dety
extremi:
x
X minor,
V major. quaorata
esit hEunctas et a, Sb sint numeri dati
quadrati xtremorum sunt XX, et sy,, quorum datur
differentia yy-xxLan summa omnium
ab 1 ad X est XX+ Xh. Et simi
liter summa omnium ab pad  e
ab
A
go ab 1 ad y-h
du, quarum duarum
yu- yn
e
summarum differentia es erit
Vy - yh
Seu (3+10)
2
XX+ Xh
2
quae _ = bh
yy -Xx + xh- yh
e
= bh unde
per 1 fit (4to) ah + xh - yh = bt seu
-X.
seu (5to) = x+y = 2b+ a. sed per 1 erat y in X+y
mop
6to) = ah. ergo per Sfit  X + y=ah
Ergo per 5 et 7 fit 2- 04a
e
=2b1a
2b+a
20 = aM, +  a = 2b Et (gno) 2X = = ah C (a. 26)
q-2b
1(10mo)
compendio sit a - 2b C fiet
a- 26
 (1mo) 2y = ah +C et (12mo) 2X = aM +C
itaque
nueruna summa iatere C
vertie
chani

## Folio 9v — 00068124:0018
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000018.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 49 lines, status machine
diflerenia Excessus data ing supra duplum
minorem ocetur su
pa
tare
a interceptorum
a
Vocetur
peratio procit
differentiae quadrato ram super duplum summa
u
su a ntercertru odivi tu per
daisferentia quad raldium dicidatur per e
diferentiant quadincorum, quo pro qd
prodit voceturm
a ipsandifferentia
24 1e 
extremorum sit c; et major numerus
ued
extremus erit dimidiam summae, minor
dimidium differentiae horum duorum d etc
xemplum. sit differentia
Quadratorum 1064
a. summa
interceptorum 5082. quae duplicata
s
dat 10164, differentia est
10b
1016
48
al
A
quae vocetur
22
O c
C.
48, er
per quam
dividendo a prodit 22 =d
+4944484
+
2s
534
22
462
231
C
erit y -
253
erit X = 23