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# Catalogue record: 33724 — Exercitatio Geometrica de dimensione figurarum Autore Davide Gregorio in Academia Edinburgensi Matheseos professore Edinburgi 1684. 4°. [Rezension für die Acta Erud.]
# Incipit: Libelli huius qvia nunc demum ad nos pervenit,
# Date: 1687-04
# Sender: Leibniz — Addressee: (Acta Eruditorum)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=33724&katnr=41195
# Work: https://leibnizlegible.com/work/00068145
# Title: Leibniz-Handschriften zur Mathematik LH 35, 9, 20
# Folios: Bl. 1 (from the shelfmark LH 35, 9, 20 Bl. 1): 2 pages, canvases 1–2, page ids 00068145:0001 to 00068145:0002
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068145&page=1
# Lines: 55 recognised on 2 of 2 pages, mean confidence 0.93
# 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.
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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 1r — 00068145:0001
# Source image: https://digitale-sammlungen.gwlb.de/content/00068145/jpgs/default/00000001.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 44 lines, status machine
Execcitatio Geometrica de dimensione figurarum
davide Gregorio in Academia Edinburgensi Matheseos professore
Edinburgi 1684. 4.
Libelli hujus quia serius ad nunc demum ad nos pervenit, mentionem.
non prius facere licuit. Autor  Celeberrimi Geometrae jacobi Gregorii
ex fratie nepos, id dat operam, ut patrui vestigiis laudabiliter insistat
Narrat quid a peto sit ab illo fuerit praestitum cirae set tum circa series
semtes inflinitus, quarum
convergentes, tum circa illas quar specimen primus. Mublicavit
ampliore invento
Nicolans Mercator Holsatus, quas postea Neutonus universaliores reddidit
Nt statuisse autem jac. Gregouium per series istas Geometriam
multo auctiorem fuisse rdtam possertim cum in quaris aequatione
reddi
iterali facile esset seriem infinitam ejusdem radici accommodatam
adhibere, et quod unica cuivis gradui sufficeret. Caeterum
anta noster  in in udversaris ejus Methodam nicempl
patru quae in manus suas pervenerint, ait exempla quidem
hujus Methodi sed operandi forma destituta reperiri. Itaque
calculi
Methodum seriebus producendis aptam sibi fuisse quaerendam
Exponit autem primo quid sint lineae vel figurae Elementa e Quomodo
secundum Methodum indivisibilium ad dimensionem serviant
idque exemplo infinitarum spiratium illustrat, idemi ad
curvarum longitudines applicat, unec ilemque ad superficies
et solua rolatione genita. sed quoniam infiniti, sunt casus, ut
ad summas ineundas Methodus ista non su valor elementi est
implicatus  nec ad summam inveniendam aptus succedaneum
est ut explicetur per seriem aptam terminorum infinitorum
infinitam terminorum aptorum, methodo supra suoi sevundium
Morcatoris et Neutoni Methodum exemplis docet 
quod exemplis docet dividendo secu cum Nic. Mercatore, vel extrarendo
fadicem cum Neutono. Idque Canchordum cissuiduqs aliarumque
figuamiuu ex implis et Ubi d seriem exhibens prol
urva Elliptica e Hyperbolica negat earum rectificationem
a quadraturque spatu pendere. Ex ribet et seriem pro
arcum circuli ex danto langente
investius a set. subiicit. firlasses notatu dignam ent pinc
cuna logar thinica et cum
Geometrae qulhocedi quiliecum meit
L
nitis cilculi quadraturam Trausact phit. Mens. Aprit. 1082 editam
consequi proestantisimi
Auitoe

## Folio 1v — 00068145:0002
# Source image: https://digitale-sammlungen.gwlb.de/content/00068145/jpgs/default/00000002.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 11 lines, status machine
qua in nostris Actis extat mense
et
ebs. einsde
anni Calculum etiam subjicit pro teginentis secundis sphaero
idum atiaque et de ipsa calculi ratione in ad summorum
Analystarum Vallisu e Neatoni doctrinam sese refert
dimiensiones autem per serres infinitas imo ler non
figurarum
minus Geomethicas statuit et in suo genere perfectas quam
prianguli aut parabolae, quoniam simplicissimas sint, quas
rei natura patiatur