# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/45145/text
# Catalogue record: 45145 — Grandi an Leibniz
# Incipit: Humanissimas litteras tuas per Cl. V. Magliabechium
# Date: 1705-11-01
# Sender: Grandi — Addressee: Leibniz
# Other printings: Gerhardt: Mathematische Schriften, Bd. 1-7, 1849-1863, 4 S.212-214.
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=45145&katnr=33934
# Work: https://leibnizlegible.com/work/DE-611-HS-973069
# Title: LBr. 324 · Grandi
# Folios: Bl. 4–5 (from the shelfmark LBr 324 Bl. 4-5 (=33935)): 4 pages, canvases 7–10, page ids DE-611-HS-973069:0007 to DE-611-HS-973069:0010
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-973069&page=7
# Lines: 325 recognised on 4 of 4 pages, mean confidence 0.63
# 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 4r — DE-611-HS-973069:0007
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-973069/jpgs/default/00000007.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 82, 2026-09-09T18:17:48Z — 50 lines, status machine
Summo Geometre G. C. Leibnitojo
Deuido grandus S. D. D.
Humanissimas litteras Mas GCl. V. Magucabechiu mita Florentis redditas sumna
aectuptate erlegi. Quque ad commodiore pralysici calculi scriptione admones grati–
stima sunt es asiri forsasse futura nis maioris obscuritati, et conjusiones cauende
scrupulus aliud suaserit; optandis eni foret iatiis signis statuendis retinendisque
mathematici convenirent ne ad noui cuiys sibet libu editione noua serpen
nograstria addisdere, et imaginasioni fijere fectores conaatur, neue mages ab suius
Scientiq culta Tharactens perglenitate et inconstantia auertantur.
Acta eruditom Lipsis difficillime ad nos, necnisi seriies desermntur F lorentis, ad deper e anno
1690 prita libri meo geometrici editione gromonens, uix punius seminoes paties
illa euduere daho fuiz in Biblisera Car Medicei, uti samen ad an usque
1694 dumtnt collecta tul sernabantur, necscio adhuc possenond tomond acce
sione lorupletan hrisse. Hictamen Ditis apud ermomu eguité Albizin ad annd
e
O.S
usque 1699 eoctersa habentur sed eatera nulla tilipentia siti potuit c
pertinacia sellora commercud omne sibligidand perturtaate. Inde non mino
aut nostro dilijentis effusere quandoque inventa vestra, qu nec stm
ad nos deveniunt, nec ubi deveneint im ob hateri possunt, ut gro arbitrio
consulere liceat.
Granitatis intentione in duslicata ratione distantiand à centro recigrore sun
crescere ex Planetan periodis, ques temponsratione sesquialter rationis d
e
sa
tians a sole otcernat, ingenige deducitis, at generati in terrestribus etia cor
on
poritus id obtinere ut peruaeammur hosica, aut mechanica ratio desice,
ratur que ab Atractionis Wypothesi, nel an tiguo alsistenate non perdeat
nec
Buc de geperalibus differentis d’y potassi amicis erius screntie studetis cemmunicabe.
4.
la hisoraer utrumque Manfrediu, saudo Victoriacara re verali
hanganins et (sperocti accessum, qui nunc lineari tantus geometria profundis
sima et sabriliscona quegne molitar) Laurensiu foren inul
Venis ad Droolema à C E0. Benoullio progoiho mihigne abse commeniad guo
quo summas tibi gratius refero, eti s uilimre me deincess prose paris expaius oy)
s
nempe de Cumria descrventa cuiusarcus arobis assnu arcul poritione
a
dato alterius geroporis Came sit equaly; Quospectaat nlaa à me edita in
c
epistola seeica adShoma Ceina adnesca demonstrationa n aremitis Hapeni
una C
anoru, quatenus iti num 1q douui cualitet glana figura tata, qu’a dugecte et
n
curna qued congrehendat, cylinorud invenire, cui ita circamucluatur, ut crua ipsa
nihilorecius in unosario icat sitque. ejus eepliida transuersa sectio; quemad=
modus excesiodiasper cycloide erecto, transuerta sectione Ratetur curica
datz paraibuts assalis adrrihiltit aeepuila csindica sypersiciet parme ad dietus

## Folio 4v — DE-611-HS-973069:0008
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 5r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-973069/jpgs/default/00000008.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 82, 2026-09-09T18:17:48Z — 46 lines, status machine
sactione terminantis, qua Dambola ipsa cysindro cycloiali aductutu; quo
C
eode moto notam Logistica ex cysiadro super Tractoria erecto secari pose
C
et generati si relatio ordinatant ad axe mutetur in recatione ordinatan
ad carna ex cylindro super posseriore excitato; priore curva secarsose
Si
id quod methers tangensia inuersa obtinetur, ad non aliad resiiratur, qua
at tansens copesiteerioris cum, suc qua cylindrus exccitandus est equetur
e
e
temper subtangent prioris curre date; sed et s’exglicatione in glatia eame
C
sugerficiei conice, contingit cuvuas transformari in alias priori conpitudine ret
vel connctutione cirra eono, aut cysindra, de quibus allos.
Verid arbitror popdrins Theorema sia solui posse: Curne dite axis este = X et
ordinata=g. mox naler iptius du interminis ab ipto da affectes (3 disferentia
nons’esquationis curne datee) repenatur, omnesque eius coefficientes gonantur
=2; idess dy = 2dX. Acis aut e’cugne date habere debens a arce cume
inveniende ratione e ad 9 lin portionibus, quibus respardetant espules areus cumes
dico ordinata curme guasite fore integrale quantitatis dx V22- 99 +
n si non curemus, ut Curne quesite et date axces certa progortione (in
Et
partibus que respondent paritus cuvuand orcubus) obtineu
r
Ootae Cumae AID ad eunde x AC apsonatur queliter curr
AHN (dummode ejus basis C non maior, sed utcuns. mi
sit data curua A2D; quod inschemmate non obserruni)
ducta valitet ordinata H2F, et cume posserioris
normali Hk prioris aus tangense E1O intercep
faso CH, et vi ex vertice garllela AB; fiat perpehe
RF ad quadrat FH, ita quadratu tangentis E. B ad ageregatis qua
dac
AC, et  et ordinata be ad basos e directo plincti H, compleatur
i
hormodo curna; spatio aut S6QTC asflicato ad AC oriatur lati-
tudo 6X obid vidinanda ut groveniat curua MXC; Hgc erit equali
dase
2 AD. Oodert 
s
s
Hoctamen deficis utrague construtio; quod non semper un gron
enadas integabilis dX V22. g + indesendeatet a curnis non reci-
ficabilibus, nec in posteriori, sgatiu 6Q7C absolute quadrabile tem
euadit, ut gpus esses ad algetraicae cums qus ties equatione
constim.

## Folio 5r — DE-611-HS-973069:0009
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 4v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-973069/jpgs/default/00000009.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 82, 2026-09-09T18:17:48Z — 48 lines, status machine
erda sed quandoque dumsanat idue es accideati, nisi metod
eces
constructione spatin 647C quadrabile grovendat, quod mihi nune
fateae
in promisu non esse nec uero nacare ut illud inguira. Vale
et de Mathesis dignitate, qua hactenus adéo promonissi bene
meren perge.
hisis fral. Noneat. 1705
compasus fatcorhe Eximu Geometrae, Quidoni Graudro
d
esset oplandus
Godefiidus Guilielimus Lerbnitius P. p.
l
Gratissimae nihi fuere literae luae: notationes Al hebraicas
.
11)1
quisque pro arbitrio institgit: ego commoditatis ratio nem
ut omniam eadem linea ignari possint. ovito super fenitat, neque enm
n
Meditationes Tuae ad Problema Ternoullianum sati vim
ingenii et detri a indicant, etsi non per omnia vecaverit
plersus absolvere quod desideratur Mra quidem
et per seripsi
solutio 2go quidem solutionem statim dediid quam
exemplis exequi non vacavit. Compisi tamen alteri
qui forlesse dabi eadet aliqugnde
hunc curam MMani ram mini in his versar ad
attertius oix ultra licet
Aliquot viri docti nunc in  Arithmetica
mea dyadica occupantur, ubi omnes numeri scribantur
per per solas notas o et 1. omnesque numerorum series
ecec et pulcherrimas in quaris columna
puliremas periodos habent. unde fit ut haec, notandi ratio, etsi
non destinata ad praxiu vulgarem, magna tamem
scientia increntienta promittat. Apparet eandem
noarithmetica ante ter mille et impluis
annos innotuisse Fohio Cinensium Regi velt grlosopho
ut ex ejus figuriis a Coupletio B aliis jam editis ope
artohmeticae meae compertum habemius, sobutum aeuigma
ndc sa
quid ipsis sinensibus jam confutii tempore negotim
facessivit
alio quam iller
Avisidn signo
ad exprimenda
Rationem t pro
portionalitat
opus est.

## Folio 5v — DE-611-HS-973069:0010
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-973069/jpgs/default/00000010.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 82, 2026-09-09T18:17:48Z — 181 lines, status machine
Hissimo Clarissimos. Vir
efrido Gaphielaro Geconcua
1C
ser Cectoris fanrove Consilia
id
l
incaoreta
cannaescr. A 
Haanem
ex A X AN ~ X ea
f. + 
8 d. S
Ex  8Bp
e
 F X E.C
18.
1) 8. b d. bct X
9 Si 8
ax ao
7G0B
a
eF. a
d
e8
5: si
e
sc
 
dadi
a
EF f1C ∞ ∞ = 6. C
∞. C 2 5
1∞
d a
vie
ed d
+0t
i
 d
ge
a
 
v.
d E 1C
von
b
d
eatZ
aus
D  BaC 
as ine
in
 
e
C5.   a 5 B R 5:, 1. B.
d 8 2
X = C E
B e
a e
x d
6. 
di
B 
a
A E
a e
 ce
5 0 5
C VE
et
pd.
a L
SC
∞P
05 
 Ex
egua
(8.
a a
e
eX e
ntc
e s s E.5
Edd
∞
 E
F
L.
s
e d p
d c
E.
A
ar
Ld X D. F
A
6. 2d C ∞F
es
C 3ED
VC
b
e
E
1E
C
A e.  + B A
o
Ek ∞ A A F 3. 2 
. 3
5.
 d  dre A a
ql e
2
.e
x 
P
  8 
E e
c
P C
s
a D A D
_ Sit
e
6 5
e
DNe 
 
en
te
et
e
d an
1c. ∞
.
2 E. E
8
d  _
e  
X
A.
D2 2
e
es x
p
d6
u
d. 
2.d
D
2
d
ec.4
LX
∞e
SFS
vsie ex
Aum ed
e
e
6  e
eux
te
e
dia 
2d
t
SC FD E se
8 F. 8 D
d 5 d 6
ec. 65
si
s
dp
de
de
e
si
 B
ee 
pt  ad