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# Piece: https://leibnizlegible.com/api/records/42111/text
# Catalogue record: 42111 — Leibniz an Johann Jakob Ferguson: Extract aus der antwort,
# Incipit: optima est aequatio, quam mihi misisti, pro problemate data summa quan
# Date: 1682-08-10
# Sender: Leibniz — Addressee: Ferguson
# Akademie-Ausgabe: AA III,3 N. 385
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=42111&katnr=31508
# AA III,3: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-iii/
# Work: https://leibnizlegible.com/work/DE-611-HS-971140
# Title: LBr. 264 · Ferguson
# Folios: Bl. 32–33 (from the shelfmark LBr 264 Bl. 32-33 (=31507)): 4 pages, canvases 65–68, page ids DE-611-HS-971140:0065 to DE-611-HS-971140:0068
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-971140&page=65
# Lines: 294 recognised on 4 of 4 pages, mean confidence 0.69
# 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 32r — DE-611-HS-971140:0065
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 33v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-971140/jpgs/default/00000065.jpg
# Model: k3-trocr@runs-615-epoch-5, run 617, 2026-10-30T12:51:04Z — 33 lines, status machine
tine cum alibiostendendum ex data summinalerum.
parti gradus et quadraturum a 4 quantitates geometr
Téngussen
dele servi
je Heere
NB. Nachher von Pom
yn Heere. Ick hebbe eer gewijmen tijd geleden
Uw Ed. Gestrs genotiificeert gehad dat de Heerck
Blauw, als noch de ende drucherije tot Amsterdam
dam aenhoudende, wel genegentheijd hadden uw Ed.
Gestr. Tractatum de quadratura Circuli Arithm
Haer
te doen drucken, edoch dat haer Ed. geerne
alvorens soude weten den jnhoud van dien, mits-
gaders de Conditien waer op uw Ed. Gestr. hetselve
soude gelieven over te geven, ende in specie hoe
veel exemplaren deselve wel voor sich soude will
aenge-
bedingen, ende dewijle ick, onlangs daer over aenges
proocken sijnde, gern. Heeren Blauw geen naerder onderrich
tinge hebbe connen geven, als ’t sedert geen tijdinge
veel min nader ordre van uw Ed. Gestr. hebben
o insinuisse in yvemice in ontfangen, soo sal ick hier ontrent desselfs rescriptum
Ergo et gel rosam pie met den aidaressen te gemeest sien.
Uw Ed. Gestr. heeft in desselfs laetste missive mij
gelieven te schrijven dat sijne methode van sub¬
stitutie van letteren bequamelijck conde geappli-
ceert werden op een Problema omi drie quantiteijten
en een geduijrige proportie te vinden wt häre be-
hende somme De, ende die van hâre C i xb.
da
sollema sexti gradus
erit seyte gradus.

## Folio 32v — DE-611-HS-971140:0066
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# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-971140/jpgs/default/00000066.jpg
# Model: k3-trocr@runs-615-epoch-5, run 617, 2026-10-30T12:51:04Z — 72 lines, status machine
en dewijle ick voor die quantiteijten stellende x, y,
en 2 eijndelijck beconne tot een aequatie y3 - 1/
t’
sijnde waerlijck soo eenvouch als immers een aequatie
Ges
wesen can, soo verlange ick te meer uw Ed. resolu-
adiens halver
te mögen deelachtich wesen.
Waer mede dan uw Ed. Gestr. in de bescherminge
sedes bevelende sal ick naer praesentatie van mij
onderdannigen dienst verblijven
et
dele Gestrenge Heene,
ß
oprima est aequatio quam mihi
pro problemam
Extract aus der antwort, die
r Genommten data summa quantitatum processionis
Geometricae di Lujus autorum ex ipsis invenire qvantitates, nomb
nempe si sit nachzuz a` ad x + y + 2 (= aequ. 6 fiet
y3 - aeq - 26 aequ. 0, quem admodum meo quod calculus exhibet, sed
praessuntae literis anni aucis maxitiori
man noch fernere, ponendo in aequales hu + ut ut ut ut ut ut ut ut ut in a` c
t’ a
et
ictum, rectimo esse ao aequ.
homoreo notoriarum a
e
gutorum sub
e
n
esse
re
equ. M.
Noth-blumptum
jamaoptiquario 16 — - d =
Ew Ed. Gestr.
et pro am substituendo valorem, ag fiet y: aequ. aequ. - '
Ita evito coaltationem aequationis, quae calculo A communi
ustingit, et cujus deinde, derum de persionem quaere etor
i
et
2
x y, 99
quod si tun calculus
Superflica
3 aequ. 2
dem pervenit, sine una itidem
exastatione
t posten
b
s
dépressionem non minoris eum aestimab
et liberir
quam menn. Sed vide
quaeso si varat, quale sit
e
lutio hujus problematio: data summa quodratum et data solum et Custorum
quatio zuilitana Geometricè quaestionatum invenire ipsas quantitates
vor
e
nistri
elementio, pro
2
3 y er y94 + 2) auch heut
d. di ermeer 16 — y
et V. aequ. f y3 + y y y y y y3 y3 aequ.
k
Hage den 23
16 M.
To
aepX + dyv + yj r

## Folio 33r — DE-611-HS-971140:0067
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# Model: k3-trocr@runs-615-epoch-5, run 617, 2026-10-30T12:51:04Z — 90 lines, status machine
1
x + yx aequ
k
x + y
n
aequ
Ergo xx + yx + yy aequ. x fiet yy + yx + x + x + x + + + x + + + + x + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + x + + +
X
ti
47)
seu y aequ. Sax3/2 xx — 1x necessaria erit
u
3
ex
ergo sequitur y esse quantitatem quae eandem
b
Gebet relationem
et,
ad aequam habet reius cubus ad
eandem et ad,
e
fqvitur, sive per sentiat.
ietzo
ex
tudo referti ad 6. et a x qvo
r
x ad x3 et 6 et ad x sed ut obiter
yrt yx + yx + yx
Aliqu
c. 3.
e
2
e. Quodem modo 1. aequ. 2 fJ xbr Xbr
b
b
X + yx + y aequ. b
das da3: -2/3 vr aequ. z
h
ft.
en
art
ss
y + y xx Amy + yv + ràr 0
yb- xx - y3X + p
v
et
equ
aequ.
v ydx - y3 - xx y aequ. 0
f
e
95 a
a
an
t
ch thodgederranda
pulara,
v + y + y aequ
dinge fy
2
x aequ. 0
ex
x
d: xy + x + yx aequ.
ex
fiet das Autor preti
jam a` vor y3 erp rth. — ex natura
a
f
y3 - xx + xx + n aequ. 0, jam xzugey yy
s
ergo fiet: x — — in aequ. v. un
ergo ayz aequ. 93
ut observicam in est möger si p. 9. 2. sint progressionis Geometrico
t, der teütschlag m
Princip
ein
V
aequatio novissimo probati
jam erzeigte seyn Hugo fidem - 3 f - dt
dergestalt, daß diegestalt
v
e
en quia nuper v. het 33 — 3mt + 3 y / vnd x et quae
veru ess
33. Jan. 15
ronipani quod
et pro infi obilitur fiet yv - ll y + aequ’h
a
cijn

## Folio 33v — DE-611-HS-971140:0068
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 32r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-971140/jpgs/default/00000068.jpg
# Model: k3-trocr@runs-615-epoch-5, run 617, 2026-10-30T12:51:04Z — 99 lines, status machine
summonus publicina difficultiren si sint quatuor quantitatis et
dalusumma quadratum d’cuborum.
n
n
ft y
n al y y muth i
VogelPago per prago XyfJBepreiS + f
A
ex
möge - aequ. alda + y (= aequ
n
x + y + aequ. a a a, a
e
in
mondio ia data 313. dyy -3/2
u. aequ
n.
jen
n
an
u
d
en
x XX
e
x2
ex
t
2
er
2 p. xp
equ. xy
e
dy
em ao
et 13 — 3 lm + 3x aequ. 6. er
e
en. Da
Ep valoresium in signo
fen protest b - pij + pl aequ.
n i
b
aequ’a -
h
l
ms n’t
von B
n,
nim
e
3
l
2
e
a= Hn im
i
2min Staekays
e
d
solte
vn (rath
ey
n
6
h
aequ. 0
d
ar
h
et quia destruitur. Pabelm.
Valor ipsius per aequationem
agendo identus
inutili,
e
e
Ecclesiastico ipsius p.
contruit semper
at abito jam
habentur m et
e hujus
instorum ex l. 11 -lyten
jus aequ. l - xergo fit x aequ. — ut xx aequ. dyjus,
ergo Uyy-ringet
4
10
Hugo Pago
t, y auch qvatqve qui
i
V
h
Uy-Umygy en
ut sulphuam conveniatur p. et
cio substituatur in ligno x + 1 + 0 + 0 + 1A2A2L1G etc. Ergo brevus
in aequ. x + y dx y + x + yjus + yJ subsulmatur pro se valor ery
v
XIX
tis sive nolum ad qualum nonum
er
M.e