# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/42151/text
# Catalogue record: 42151 — Detlev Clüver an Leibniz
# Incipit: Non adeo ingratas Tibi fuisse meas de rebus Arithmeticis literas, resp
# Date: 1680-07-26 (80-07-16)
# Sender: Clüver — Addressee: Leibniz
# Akademie-Ausgabe: AA III,3 N. 089, AA II,1 N. 227c, AA III,3 N. 89
# Other printings: -E1: Pasini, E.: La Nozione di infinitesimo in Leibniz: tra matematica e metafisica. Diss. (masch.) Turin 1985-1986, App. S.49-51 (Teildr.). -E2: LAA III,3 (1991) N.89. -E3: LAA II,1 (2006) N.227c (Teildr.)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=42151&katnr=4954
# AA III,3: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-iii/
# AA II,1: its series at Leibniz-Forschungsstelle Münster (online after accepting its terms): https://www.uni-muenster.de/Leibniz/seite5.html
# Work: https://leibnizlegible.com/work/DE-611-HS-958501
# Title: LBr. 163 · Clüver
# Folios: Bl. 1–2 (from the shelfmark LBr 163 Bl. 1-2): 4 pages, canvases 1–4, page ids DE-611-HS-958501:0001 to DE-611-HS-958501:0004
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958501&page=1
# Lines: 123 recognised on 4 of 4 pages, mean confidence 0.86
# 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 1r — DE-611-HS-958501:0001
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 2v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958501/jpgs/default/00000001.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 82, 2026-09-09T18:17:48Z — 41 lines, status machine
proposui problema invenre
tres numeros quoum
si
sit quadratus
norum
Via Amplissime ac Consulassime
Non adeo ingratas Titi fuisse moas de rebur Arithmetics lteras
responsoria tan videntur innuere: novan, ut oides hine arriori ansam
sprasertim data occasione por De. Hannium) denuo te intorpellandi
ac sanc veropportunum acndit ,ut aliquot abtine diebur D Hanson
Exhorum junoru comitie Coniginarts de instrumento illo tuo Arithructico
disserenton inaudiverim, affirmabat ipse eam mactinam multu constane
rotulis quarum artifivosa revolutioni opirationes paquam deptie queant vertici
e
d tanta faulitate, ut vol maxime otissus, ex Scholactico subto in Archimodem
vol Diophantum quondem transforncari possit. Negi est quod aule negotia
Tuam in dea absolvonda inductriam remvrari amplius pernittas removenda
cuin sunt illa Philosceliai diverticula, qua hunc luci tanebrar offundunt
Magne interim sini dubio sunt astimanda quae in expositione analytica dioota
te invenisse scribi certe quolquot extant ejus commentatorei vipdum scopua
beac videnqus assecuti, neque Hylanter, Bachitui, Fermatias, Bilus, omnt duc e
ali eam quam promitunt afferunt declarationem. malti erim adsuredum
rectant nodi dessolvendi, quorum uscri est pereximicus. Exompl loco sit eligans
Ilud problem quo trei quatuor vel quin numeror quadratas invenire jubemur
e
quorum summa vet differentia sit itidom forma quadrata. Diophantur _ad
quomulibet summa et differenta eo reliqui ingorsertum hic afferunt solutionem, Tito autem quia melior sit
cognita syntlosio laud dubito. Sicuti e novos ilor claractercus, quorum bincfia
a summa e rectanguli quoruns numororum po sol inspeitionem detes
ninare potes, elegantissinos esse crodo, quanoi contraria retion. jam obm
(nullos atdendo novos) reliquas quar labemae figuraue arthmeticas ad similicec
illac o 2+ retureato. farilimam quandam Lini extrii posse logisticam depro
Rontaim, qua per progressionim duplam nullo sit obnogia mutplecationio vol
divisionis taedio. Verum Athiorem fasan lavabit, qui nova quaedam huc dere
acta nasa Orbi obtrudere vellet cum altera iim signandi numros consoctudo
utique jam sit reoepta. Regulam illam diagnosticum, qua Entia prim a compo
sitii discornuntur nullum Pliloscihoram aituedum detirinare potunt Cartes
hic ingenue suam professe est ignorantiam, _joi in tactandie numonis longe
eo peritior fuit Fermatius frosta in ciu indagationi desudavit. Cirto req
est haud levic morvonti, qua humano intchertui prima velut mundi stanina
suppoditare potent. Algebur est pofectionio dum nocusat, ob difficuliarom

## Folio 1v — DE-611-HS-958501:0002
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 2r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958501/jpgs/default/00000002.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 82, 2026-09-09T18:17:48Z — 37 lines, status machine
soloerdi problemata itla quae passim pro desperatae haberi solent hominum
votoue inscitiam te objungare cridoherim, quam vulitrae hinc scientia na–
voc ac defectui exprobrare velle. Neg enim sequ mea salten opinione) dantur
hujusmodo problemata qua sint transcondentia h. e vel omnis vel nullius goniri.
Totum siquidem vitium in eolatet, quod Algebro scri itorci mondum penitus
faccint admissi at amplegus hujuc amasiao perquam scmpulosa, ploros eua
omnes subsistore uodeas in limini, dum partem itiam Eopis nad nagina necesse
riam quomodo sciicet quibus modis aequatio aliqua sit ernonda,  quanaa
serie una demonstrateo ex altea sit deducendu vel plane negligant vel
param excolunt. Lumini enim Ratiomi nihil non perviam est cum st
ipsias divinitalic inago quoedam absolutissimca atqe per disquisitionim nfiniti
rativum in se resusdit et splendorem. Statica auton sive siientiae ponderand
persimilir videtur hac Algebra, qua scilicet ex notis ad ignota proroditis niqu
seri ex eo quod multi in patera puurtum applicatroni determinare hani
possunt illico tota vertur labomoxisius arguenda venit metiotca nen side
distributiva quadam cognitione opus est, sot quam frustua penis ilos autorei
Laram rerum cupidus quaesiverit. Ego sant per nunas ambages tandem
deirchondi principium ilu doxiao, quod omnibus hartema obicim posint ninime
suam
ex algebs vitio, sed ex insufficienta datorum e defertu ordinis aiginem tratisse.
D.
neque enm sut oulgo silent) per tot intricatas demonctationes, res pes literas Alplabai
mathematicum illum caltulum expodire soleo, sed numeri plane absonotimrtu
universalibus, tum nethodo intelle ctuali (quae gradu sugerat scentiam, priaa ex uterma
 aece veosa deduco, quinimo videbis sut sr hcor) quomodo por olam quantitatu
seriem ex cessivam ac defertivam omni Frigononetriae problemata jerunde possinit
construi, atq unica pera innumei casue limitibus constringi. Combinatoriam
quid attinit, num eandem simili locum sensa arripiam, haud liquet nihi enim
est stiertia illa plastica Naturae, qua omnium reram quas mundcis comploctitur
varietatem dinumirat, ac loges compositionis sive congressur cum terminis figum
rum designat. Eargit autom haec scientia perende ut Arithmetoa naturali
ex insinita hnutatis replicationi, quae deinte infinitas producit potentiai, quas oe
Mgebrae dividimus, exquirendo in quanam proportione illa dovauru concurrant
acquanam metathisi connectantur. ex. gr. su quaratus illa idea unvirsali qua
rei quaterao jungit adii ea sut nothi, foracatur qio  partem potontio coto
minus ix pol. at:  pt sorunio =  postertio quiad. sie N + N3- i
deragonum prismat se recondit, speculatione dignum; ac recte ex

## Folio 2r — DE-611-HS-958501:0003
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 1v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958501/jpgs/default/00000003.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 82, 2026-09-09T18:17:48Z — 38 lines, status machine
conbinatione simili potentiarum, quiequid abstrusi in quormetia latet eruo
potect, omninum sigurarum proprietates longe alia ratione involoscunt
quam vel ab Apolconio aut Arch. n. ode sunt demonstiato. Linguam
iliam Philosophicam vel cabalam figurativam hio frustra in augilium
eum
vocamns suo enin loco relinquentam conse donce omner reum
differentio in hacen fuerint protacto de iis enim quod moni humana
pordum nisi supisficietenns agnovit, vic intina sperinda sunt vonunta
inpriois
per re; itidem esternat, mi rebur insipidiis adhuc panso plecnm
inponore hiet, visi rationis currum invesso ordino insta illiur in casa
equos
quis
Calisti circunagere ac postica jungere parti conveniens durent, vomum
hisce dintius taam hale desonere volo exic. Mea qua sint polimini
p quomodo novarum Gilendum construationem in usem sendo vorturi
aggressui fuorim, ex catilogo franeosunters:, si placet porcipore pcter.
Res geometricac  optocas postita lum expositurus sum. Valo ad  nisi
molectur fuerit rescribas quaeso, quon an aogule culi influgur vectes se
ingorant vertici; Hannoverami enim sdi elevationem ua expirientia
statilitam vellim, distantiam quoq vestri loci a circumvicinia paulo exacto
n’nonsura explores rogo.
aba Lordiut
26
A 1680
Amplissino J. No
ad
C
eris
im
sercabo qui agat ineom
eu Aa
ex eo enim tempore, quo hic sum commonatur
ipsum merdum oidi ab aliao saltom aocis.
Lcgariltoir adteot vesan; sastitution
n
vidisse puto.
eo

## Folio 2v — DE-611-HS-958501:0004
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 1r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958501/jpgs/default/00000004.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 82, 2026-09-09T18:17:48Z — 7 lines, status machine
C
lin
obilissimo aque omplissimo vica
Godofredo Quielmo Leibnuzio
a v
rano a Cons. i
annovo