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# Piece: https://leibnizlegible.com/api/records/27656/text
# Catalogue record: 27656 — Leibniz an Johann Jakob Ferguson
# Incipit: Deßen beyde schreiben habe zurecht erhalten und bin deswegen nicht wen
# Date: 1683-08-25
# Sender: Leibniz — Addressee: Ferguson
# Akademie-Ausgabe: AA III,4 N. 014
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=27656&katnr=31509
# AA III,4: 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. 19–20 (from the shelfmark LBr 264 Bl. 19-20 (=31500)): 4 pages, canvases 39–42, page ids DE-611-HS-971140:0039 to DE-611-HS-971140:0042
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-971140&page=39
# Lines: 309 recognised on 3 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.
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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 19r — DE-611-HS-971140:0039
# Scan: The same scan is also registered as fol. 20v; its text is given once, here.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-971140/jpgs/default/00000039.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 317, 2026-09-10T22:15:18Z — 192 lines, status machine
Habita hac Tabula qua nullam in algebra elegerutiorem atque nciliorem scie possumus solvere problema genente
sequens moxutile futurum: Data aequa tione aliqua, invenire atiam, cujus radices sint quadrata vel cubi velatiae potentiae dat
vel et etc. radicum aequationis 9a. tae. ex. g. sit aequatio dit gX 4Z aeq. a cujus radices
 C - X C + y aeq. 0. cujus radices seu duo alternali valores ipsius e sint a et b.
sunto a. b.
patet X (secundum terminum aequare a+ b summau radicum, et y (tertium terminum) aequari binioni
seu e e 0g.0 et e - b09. 0)
dele sistringe sture
radicum ab. quaeritur alia aequatio ca cujus ratices sint a et b. e incognita ejus erit e. est enim e a aequ et e- b aequ. quas invicem ductas intelligendo
1c
ilemque pro aC2
et - a C + ab aeg. 0. et pro a+b2
substituendu valores ex tabula (faciendo Z et col esse 0. quia duae tantum sunt literae a et rb) habebi
e aequatiotalis ita scribi poterit:
P
a seu ((seu a +6) aeq. X - 2y. et ab aeq. gy. Ergo scribetur:
e
C- X  + yy aequ. 0.
+2y.
Si in aequ. C - x e + y aq. 0. Esset e irrationalis cubica possemus
scribere cb-
liiu Hlecia.
+3xy
ya.0. et sublata erit irrationalitas
mplex
tantum entent i quadrata, et ita si e esset irralionalis quadralica sublaturveteu dat au Mricuverta aengenomen hadde
ocedet
foret errationalitas. Eodem modo pro irrationali cubica unud aut alia quantunque cuna methodo
neam irratiulales
nam exhis
scebendintantum termines tantum ex Tabulo describenda Et si plures sint
una tilletur post aliam.
exs atemadigatione ad scifitue
abludere.
problematibus
novissuva
Nechodus
inde profici
est inveniendirado
qui
et fiduatur 
perfecte
Nes opo
cogniti aequationis
est ut plura addam putem enim mentem eeo Cd: hetto:
ex eximplo e de quo dim ad caescripseram, et quod corarist experaueiam cum te mogen becomeni edvit en hable ick 12e
irratumab aquationes irrationales reducendi ad rationale ita recipioce
idi ad irrationales hoc
redutem
calculus; et descrehendi
 si quantitates a, b, C,
Ubi notavi rem mira
cenge rescriptie dacr op te mogen ontfange. ht
eaeque sa +Yb+ YC+d nobis essepvalito nius dam. doeq arcerey, as dast uuo Ed
ponatur relatio inter ipsas a et b et C et
illud t illud mirabila hanc
s
bactru
tantum nempe perinde ac si esset tantum C aequva.  seu non assurget
d cujus rei gratio est quod quae hae quatio aequatines quatuoo quantitates cum
aequationi quodammoto pro coincidentibus habentur, itq ut uina vrrtualite
est nos
in quolibet fradu per talier radilem e aeq. 3 sa +
vum gedmaten vependiri eando mogea avpherd
sunt q radice unius ejusdemque
desimipt aquatu rationalis
e sublatu aequatione irratiogalitate at non assum et altius quam si
L
e aequa+0
eaego a+86 ubi a et b. sunt sempe
radices eju demaequationis quadeatique, at e est radix aequal
fulli pota nis cubicae vel sunesolidae, ve
led boress saies se recae
ad
uniarndu et
Et ita ex aequ. evysa+
antionatitas, ut e non assurgat getra etum gradum, lam tamen ado qui assur
ere debere
d23
un
sac gecome
cteni Cnde devjre tvap dice
et ego lubaris submittam ex schedis
perficiendo tunc
omnes. Hinc autem aditus habetur ad Melhodum generabem resolvendi omnes oecke ot sorabant
radu
b ieaque quod scribis te posse plurimas aequationes
meditationbitz quae
sorifacere videbuntur
Tos ometerdam comende
ad aequationes dimensionum, hechatellerir interventu scilicet ab tactind ve hem Van Rieuvertre dacr veder over neugen
ut sci  ponendo eaequ sa + b +C+Td habe debel vator
aequationem quatuor dimensionum, nempe a +. a+. a +. a +. 590. Sproockenben. 500 habbu iL, fit pelves arro B. Gaet
imo et re literos facile consilia conferri possunt, quiam
intelligentibus panca sufficiunt que rudmodum ex
ota etc. inveniri debeant et quomodo condi queant Tlabulae quarum witten adviterem, met verocit dat de rcu
iuna c
omniaque per progressiones eregantes procedant, exponere
non eam Epistolae foret quam dissertatiumenta. Idenitud pun
soleo ut prolixo calculli labore resecto, ex legibus artis comnbinatoriae per Tabuens et piogressiones
ce certa serio progrediente
vaesitu
esento
possulca
a
minutionem generalem regulas proset restlutivinbi
e
de
resobntionibus, omnium aquationum in infinitum interes intundis imum erit videres
suo a tuo anxulid
aldiam tud noch 200 geluckiili iet geocert van
 sit aequatio  C x lermeruerpaeq. o
rest  eaus valor eaeq. 3a + b+ Sc + d.
nisi peculiars, quadam
e
G
spe labor calculi  fere loclatur, 
protinisis
sraituetje 10 doen danchen, eude
on intelligi. Quin et suspicor melhodum tuanos non multum ab sta aliecu vereangende vas het relve temacriten
Quemanmodum autem ita habeli
debet mathoisus aequattares rationales inver
in. EExempli gratia
radicis
euum calculus. non altius assurgit quam
ultia quinture gratumu.
a inveniri possie per
et hujus aequationis
penitiam exploratum habeo
e labulae isteus nsum sriam hunus usum etiam insilvendis quam compendio sissime
su
ubi si vellamus ttere irationales ex istae aequatione
quae ex ipsis fieri potet
sint radves ejusdem
quintraritus reduce
dimiensione
4
cuius acumen, et nnec set
di
viceapum nos esses perspicere potuisti.
deprimi possit
depressionem obdiner
esset unicam d tane
includat relius vas
pantes
a te
1.
altissime Sascendendum
cujus quarum ope
aequationis tata
aequationes
radicis pura
du
Stet ryn nu al ccnge
maenden gelede. dut ich deselvo hebbe laten
et ita habemus modum aequationem datam exaltundi verbi gratia e xe ty aepe ex altandi ita ut priorum poteentiarum ipsique e
ut li pro litera
gemerali
et n
a
 quaerenda
ad
amus
perventori
his ipsis facile agnosces
-
syn megnnge dienaeuguende ten ceriten galiebe
te lateu toecoren.
Austaea irio der eraist der bibrerten in Golland sin bitte osube-
sscaesit hn bricstu
iL hebbo ooik in de gem: mijnen bri tio ede
 dio weindtums gic is machen rassis habet dac caenstir auf neho als 440 shucs soniis su ettr. Aoegeronden mipre solutiem up de aequati
od
2
a
omnu
eto grdu
Vausdex can
und stellet sih altoreit rebst in taeind, werlihos schohne niur zeit bcho gar nett gethan uniben strllunns eront
quid in
dan rnseus s in Golland daq Waeastro agdam a Rompus gar t zu alpltcia segu
eurdei; und eaeaim manus sbechib zud veno solchen 1HM Augu woeta, waeae die senge dandu his
mic nub masee don aboist Erpsickt se caurdo 06 ubeo 20 a 30 esh aecht mcosostu ali son
clanus moler
a6 nissein Tollandus riglam
din prorlemata gam i
wanucer Vp+9-Vr, off Yp+Vg-Vr. off
da so tasse mio vnomases propomet wwrun aug mehr ribio eent
Ip + V9-Vr, off vel Vp +Vg+ Vr - V5 ∞ Iyn 0
est menr remostent in Golland
nngns habus tiondte damit mansolise weasteoan pompande 2HM
mis sete hu martus nd fius sabe

## Folio 19v — DE-611-HS-971140:0040
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 20r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-971140/jpgs/default/00000040.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 317, 2026-09-10T22:15:18Z — 28 lines, status machine
waer van ik ooch mjne methode met do wtiver-
cinge 500 hacit de tyd inta ue toclates uo Ed:
Terti: tae communiceren; Do Hier Atudde hucst
my gerechit suta al voor veel jaren wvtgevonden
Ae hebben, geliick my ooche dienaengaende in
hiju gedruckte brieben sjeti getoont suess; maer
avare
altoo nijue boccheus mn des Hargo eigai in nit alle
dage naer Brabant Etont de vertracken, en
hebee il tula met connen macrricy, altroevel int
incene cenige redes te hebben van te denches dat dons
higu Cd Regueem de aequatie mar gecomposcert
aet dooc de myne vallen; waer vas des modiit einde
Truo Ed: Fertr: medo cen svave ral connes nemen
meut
Sit habbe vock not gebondem Reguleri om alle aequam
tieu van viiff dinieurien de brenges tot viere-
dibmenties, ett: 500 dat uk vel venritien saude
vederom 500 gelu Lik Aee ruogeu weter alt voor heenen
var met cuo Cd. Schtr: 4e mogez confererey, aes
dicik ccrterey. veto dat 1oodange racites ver-
brangen
der tonde auvore, alt myne melancoere uy
faclaet 40 doeu.
Tot Breda eijude, endo de minuoe fortificatien
aedace beriendo, subbo iit ouder auderen gerien den
a effectem van vecle ende verrchcsde water,
slang- moem door de wint gedreben verdende

## Folio 20r — DE-611-HS-971140:0041
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 19v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-971140/jpgs/default/00000041.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 317, 2026-09-10T22:15:18Z — 89 lines, status machine
Monsieur non lie honnoré auy.
desten binde phorbu dewalche met reedeliy. Lo wint ongelvoseyk vece
a Zuaerest nosoltu uno
sin dbcaerque incstrniqvateri opverpt, ja meer dan 3 Ketting moeeus,
sroebundu. Zeeurde anc
Gabe Hivisfasoet ghabt en, getir. L de .
nhnibe bis ich den
dac wrrck vor 7
 Rieverts in
onte form
geucha hecst, geen 900 Siguduelders comt. te
corten; en trad dat macl noih mades inbentie
gebracht, wen dic ick vermits niiu vertreck miet conde rieu-
sb doch wrrde
lsin solihes vor ende
int verche. Hecled
Emplicem sermns signie is sihi distrchiret bin. Stromene ob aber zil generat zu marhu
6 jusors iicst coose.
unt de Arte inveniendit in universum, und et Ascrentrae humanae inerementis
also dast mane quadiad. Gerti: Quede Gratio recommanderende nam
tura un deryichanir
ex specimina dazu siraerentatie var quun 0otmordiga dienet
dmum slisus, werbisis angenehm esyn wieo, als ein tractatus prie mlathematiens
verbliiveu
Quoad Sublationem irrationalium ex aequationibus memini aliquid haberi in dui Huddenti Existolu
50 verum ut ipse ait Huddemus methodim generalem ordinaliam, non compendia contines
quae hic contrahendi calculi causa omnino necessaria sunt. Et Methodus per multiplicationem
longe compendiosior formulae irrationaliptalem ut productum careat irrationatitate
Bombellus mi
adives et quam olim in quiousdam casibus etiam adhibuit Raphali
longe compendiosior videlur Ego aliam ad huc haber
jam oim condidenam, et ejus initia quaeda
sit X aequal a +b +C etc.
C
si
scendere uemini.
et yraequ abc + abd etc.
et ita porro.  compendio tautem quando
scribo a intelligo omnia quadrata seu summam ex a +b2+ e Bc et  cum scubo
A et co aequ abcde ec.
a similitu
15
binionum,
cero
tabulanii habeo, cujus intia sunt
quam Tabulam confinuare possum in infentum.
a. aequ X.
.
abxa. calentum nunc non ad manus habeo, nec
similiter alia tabula qvenda pro
ab aequ y. ab aqu.gy
denno subire vacat, non vero est valde difficilis
abc aequZ  abe aequ.
mililer
in srere
Baqu 32ab
abChaego.. faequ aabc+ 2abcd uosu
et ita porro at ita ut quaevis summa potentiarum
et
adinatsquat quaebis habeatur
ehabeant
tan omnans binsionum, texnio
per sols summas conbinationium. simplicium
empe, quadratu
a equ X - 27 a aequ. X -  3Xy + 37 a’ aeq. X - + xy + 4X7 trgy c
tis positis
ubi
motens, ende by die occarie gebbrerveert cen  dependam des 31. Sueat
re judicio tuo. e pendet
enim ab elegansssima quadam Catrula hestemcaliogo totudris lubem ex parte
darrium ex runge Waermedo dem afferceckende a intomius in Etao
votabee dinge husagus
mitu quam fuc
pr
et sy aequ ab + act ec
A
verte
seu po
olas literas X. y. Z co ctc
Vio Cd. Scir: oot meedigen cudo
ecer verobliqeendem
a aequa. Z atra
qua baqyA
d
pericient
eq. 1
Srer
t
e

## Folio 20v — DE-611-HS-971140:0042
# The same scan as fol. 19r (DE-611-HS-971140:0039), where its text is given.