# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/37872/text
# Catalogue record: 37872 — Leibniz an Oldenburg
# Incipit: Duarum tibi literarum debitor
# Date: 1675-12-28
# Sender: Leibniz — Addressee: Oldenburg
# Akademie-Ausgabe: AA III,1 N. 070
# Other printings: vgl. LAA II,1 N.121 u. III,1 N.70 (B). -Peyroux, Œuvre mathématique 2, 1987, S. 10-13 (frz.).
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=37872&katnr=38353
# AA III,1: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-iii/
# Work: https://leibnizlegible.com/work/DE-611-HS-860722
# Title: LBr. 695 · Oldenburg
# Folios: Bl. 37–38 (from the shelfmark LBr 695 Bl. 37-38 (S.1-2) (=38354)): 4 pages, canvases 73–76, page ids DE-611-HS-860722:0073 to DE-611-HS-860722:0076
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-860722&page=73
# Lines: 256 recognised on 4 of 4 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# 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 37r — DE-611-HS-860722:0073
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 38v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-860722/jpgs/default/00000073.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
Noc Aenotiosedue
uarum tibi literarum debiter, rogo ne sequius interpreteris
silentium meum, soleo enim interrumpi nonnunquam, et haec
studia per intervalla tractare.
Quod Sschiruhausium
ad nos misisti, fecisti pro amico; multum enim ejus consuetudine
delector, et ingenium agnosco in juvene praeclarum, et magna
promittens. Inventa mihi ostendit non pauca Analytica et
Geometrica, sane perelegantia, unde facile judico, quid ab eo expectari
possit
spero Germanos nostros tandem aliquando excitatum iri
tuo inprimis exemplo et exhortationibus.
Schirnhausius
nunc in Gallica lingua discenda totus est, quod eum impedit, quo minus
statim absolvat, quae inprimis de Radicibus irrationalibus meditata se
habere dixit
jam deu est, quod petiit ut TiBi scribenstogarem
pro ipso veniam silentii, adderemque ejus nomine diligentiam ipsi in
quaerendis Robervallianis Sascalianis, Freniclianis, non defuisse,
defuisse ex parte uccessum.
Elementa Robervalliana
a me ipsi impetrata sunt Msa. Legit sed milii asse nsit, qui tanti
esse non pato.
Debebant excudi, sed nescid an non mors
autoris operam sufflaminaverit
jactura certe fuerit
non magna, alia longe utiliora extare puto inter ejus Msa. Quae
ab ipso legata sunt Academiae Scientiarum Regiae, et executores constti
ab eo nominati Blondellus, Picardus Buotius.
Robervallii regiam obtinut idem Picardus.
Professionem
Rameae nesevea
 quae et ipsa ejus morte vacat,, nescio an notum Tibi
sit institutum.
Detrus Ramus fundavit hanc cathedram
et pecunia apud urbanum Magistratum ( à la maison de ville:)
deposita, testamento cavit, ut dignissimo petentium conferretur;

## Folio 37v — DE-611-HS-860722:0074
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 38r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-860722/jpgs/default/00000074.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 24 lines, status machine
Praefectum rei n ercatoriae
judices constituis Principem seuatus, d vocalum Regium tet nescio
quos alios. Itaque Schedis tota urbe affixis publicarum est, proximo mense
Martio adjudicatum iri hoc munus merenti. Haec de Robervallicuiis.
Sascalianorum Msorum facta mihi spes est.
Frenicli triangulum
Rectangulum Numericum praelo paratur cura Mariotti, qui non paucas
proprias observationes adjiciet.
Elementa Mathematica
Johannis Prestet (qui apud Malebranchium agit, egitve:) prodiere
tandem, magno satis volumine in 4. Intus vero non nisi Arithmetuam
et Algebram repteries.
Probo Arithmeticam per literas expositam
id enim potent Arithmeticis reddere symbolicam, familiariorem. Probo
quadrato
etiam casus aequationum  quadraticarum particulares secundum Cartesii
regulam ab eo calculatos. Caetera omnia pervulgata, et eorum quae
vos expectastis, nihil.
Praeterea nullum problema difficile
solutum videbis, ac quod miror, ne exemplum quidem Geometricum
ullum allatum. Ita non est, quod putes quicquam vestratibus
praereptum; Dellioque aut Neutono, aut Gregorio inbyra manebunt, quae
de resolutione aequationum per sinus aut Logarithmos, aut series numerorum
infinitas, pollicentur. Quae videre aliquando valde qvellem

## Folio 38r — DE-611-HS-860722:0075
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 37v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-860722/jpgs/default/00000075.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 88 lines, status machine
+b
X + m
X + bm + C n
X + Cm +n
X+ bmX + dem
+cm
+ bn
X +b 2m X bcm
E
mn
X +
X +
X +2n +
X + 2n X
n+ n
in - n
∞ +2m X +Amnx +
X = + 2 m X + M
m rn
2
1
.
mn
2m
+OmX
inta
+ b ∞ m +C∞ mat, p.
13 + n p 4+ bc5 un, m
n
mo
X + min
Et 2ma
+b2 m
=bc 2 mnen  9.
Ergo mere , 4 +  bc ma
+2min
Crma, +p. Ergo in tn
+2
+ b
2 mh, + p)
bc mn
intn
2
3mt  in
+ b s n
+2 un
1b mn +P
Fbc
=b3 1n42
+ b mn + PB 2
seu
c
2
emn +pH
Smn+ p
g.m+n
en em
 CB+ BPS, DB. quaentur cuva AC ex data AB. F
 _ y + dy HZ sine Sy+ YH SZ
V.2)
seu 2d men e Gner + ex ma
et emine +pun  9mn
Imn- pin ei 49 men - exmn.
men
BPH =Z. eut a dy y a fei: y + dy y eZ poone Z F 3 ad fiet
d
X
X y+1 + dy
dx N ed vel
a
dx
Sx + Sd X + y pSco ax
est autem: Co p  et fiet X + y.  saZ 
solutio problemalis quodammodo per seram infucits
tumatur y2 bX + CX + dX3 en eut Hy  b f +2CX +,dX 
et b + b F + 3d X i Z. datae e + nX + pV M
+
C
unde compar ando invenientur b. c .d en
et tandem per vyressum ex serie instiaita curva finita
in Aservationibus opus ex euplrs. Subtiles hominum illisiones dumnalius proba dicit clii
respondut futtic nal iositate, ad dueba magistina navis trapectordae toties in
allia ia fusse, nec loqui Gallice. respondit mihi aliquis satis loqui gallice cum de argenso
posutando agitur. Si quis aut si a scrpe sic respondet, aut i aliui, se q cum vipricassicit
+p
n+n)
+ a
et

## Folio 38v — DE-611-HS-860722:0076
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 37r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-860722/jpgs/default/00000076.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 107 lines, status machine
Formula plena
inferior
X
Valorassumtus Radicis
M X +b M
X
C mn
= m 6F0
X X + b v X 4 - bm
Aequatio factitia
Aequatio factiti
ordinata
Aequalio
X
LC mn
rnor
+b2m
X
Fc a mn.
X +  PX
inn
= b2 m
+
im
quae aequatio  resolvenda, ut comparetur factitiae, hab singuli termini singulis,
resclvenda
fiet: +b a m. + C mn 1) p. et pocendo
et
+ b 2m3
 n3
=ba mnrm H9
Quarum duarum aequationum ope quaerantur m et n,
m in p p
n’∞ mnB pm
9 13 et 9 - n2 + mn s pn
et mM n3- 4
n - p
m3 + n e 1
et ut novissima aequatio
sed ita ut aequatio novissima, secundum quam alter utra earum (nam perinde est)
invenietur hanc habeat formam: M.. M
epe quantitatum pro arbitrio assumtarum
X
b et c
.. 0 quod effici potest
ponendo enim + b - 1 10
sive b H 1 item = b 10 seu bp - c, sive C1 = 1.
me - 4 mn B p
statim inveniuntur.
L X b (. m. N C X
C lo. In. m
e
tunc fiet:
et m3+ n. n4. Unde re gula Cardanicae
a l. m. n
e em. en. Ben s
lmn
radices irrationales posse
Certum est huc methodo inveniri
debere; itaque tarotum quaeritur
quae eligenda sit eliminandi via.
In hanc rem proeclara habetur
ratio, quia enim necesse
est omnes a vias pro
altioribus necessarias, incipere
Jam tum in inferioribus, ideo
enumerentur viae omnes
in destructiondem in inferioribus
quadrotica e cubica,
qua cum sint parcae
scilicet et quadratu- quadra
fica quae cum sint paucae,
ex apteris illas quoque reperiemus quae
in cufi nitum progrediuntur
Aequatio data resolvenda X3 X pX +9. 10 careus secundo termino compendii causa, quia is semper
tolli potest. Huic ut similis facile resolubilis
construatur, sit formula plena inferior
C
nn
M 
-8
e
mu
.
M..
n
1
quae multiplicetur per valorem assumtum
n- 2973+ 9
X H in + H sine X - m f0
e
..
=c
l. m. n
-2lm...
C3 Cm.
=36 Imn
f, Vmn
re lmn,
et m
N- 2pn + p
tnrin
+c. 11
ter tm
+ F Imn
c
pemn