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# Piece: https://leibnizlegible.com/api/records/59882/text
# Catalogue record: 59882 — [Math. Problem]
# Incipit: Invenire tres quantitates continue proportionales quorum summa sit [=
# Date: 1682-08
# Sender: Ferguson — Addressee: Leibniz
# Akademie-Ausgabe: AA III (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=59882&katnr=57585
# Work: https://leibnizlegible.com/work/00068197
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folios: Bl. 72 (from the shelfmark LH 35, 13, 2a Bl. 72): 2 pages, canvases 143–144, page ids 00068197:0143 to 00068197:0144
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068197&page=143
# Lines: 44 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.
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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 72r — 00068197:0143
# Source image: https://digitale-sammlungen.gwlb.de/content/00068197/jpgs/default/00000143.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
Invenire tres quantitates continue proportionalis quorum humma rit ∞ a, et (uboruum Xb.
sint quantitates X, y, Z, erit qu X + y + Z∞ a, et Z ∞ a - x - y, porro sit brevitatio
causa a - y ∞ V, erit 2∞ V - X, que duita
in
ergo
et
re
Vn = Xn∞ yy Eivo Xu - vX + yy ∞v.
X∞ =V + V200- yy prima
2 = X ∞ LV - V  v0-yy tertia couantitas
Carum Cubi igitur hunt
00 + - 0012 00-77 +1=0800 -yy + etc:
s
23 - 20014 00-yy + 1107200-yy = et:
2
+
= V
e
+ 3VX , 02 - yy ∞ b
live y + 2 -3Vyy ∞b, et lubrtitutis citerii erit
V+ a - 3 aay = 3 aYY - - 3ayY + 3y - b. ∞0
Eive a3 - 3aay + 3y2-b∞ 0
Tive V = aay + = a - =b = ∞ 10.
Mea methodus.
1)
XAy+Z = a X + y + 33 = b NG et XZ = yy
sit xy + XZ + gZ = M Ergo per 3 et 4 fit Xy + yy + y2 = m. et per 1 et 5 fit ay = m
)
rursus generaliter a = b- eM (per 142, 4.) jam Xry9 Z+  3Ma + 8XyZ 2per e.
jam ex Tabula Theomematum mea  per 1. 2. 4 s. b e2)  (7) Sa y()
A
a = b∞ 3ma +3Xy
day 
3
(per 6) (per 3)
Artis est ita calculum
instituere, literasque
ita assumere ut in
calculo irrationales
destruantur. Quoi
hos loco fit
seu 3 -ay + a - b =

## Folio 72v — 00068197:0144
# Source image: https://digitale-sammlungen.gwlb.de/content/00068197/jpgs/default/00000144.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 2 lines, status machine
OTTFRIED WILHELM LEIBNIZ BIBLIOTH
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