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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 2
# Folio 1r, page id 00067994:0001
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e Dimensionibus figurarum
in veniendis ta
Signum est perfectae Analyseos, quand
aut solvi problima potest aut ostendi
ejus impossibilitas quod cum nemo
hactenus praestiterit circa tramsmuta
tiones curvilineorum in rectilinea
patet in hac parte imperfectio
Geometriae et ipsius Algebrae, quae
uti hactenus tractata est, ad talia problemata
non porrigitur. Excogitavi tamen jam a
multis amnis subsidium Analyticum, et
amicis ostendi quod huc redit. Notum
est interioris Geometriae peritis, data (figur 1.)
qualibet curva AFC (ex illarum numero,
quarum natura seu relatio inter ordinatam
et abscissam per Aequationem Algebraicam
seu certi gradus exprimi potest, quas Cartesius
appellat Geometricas, ego ob graves rationes
potius Algebraicas appellare soleo) posse
aliam inveniri curvam AGD, etiam
algebraicam, quae op cujus figura
ope prioris possit quadrari. Idque fieri
potest multis modis, exempli causa data
curva AFC, potest inveniri curva AGd talis
naturae, ut rectangutum sub FE ordinata prioris curva
et recta constante H, semper aequetur trilineo
curva posterioris seu figurae AEGA. vel
ut rectangulum sub FE ordinata curvae prioris
et abscissa ejus AF aequetur eidem trilineo. vel
aliis modis infinitis. Priorem curvam AFC
voco Quadratricem, posteriorem AGd. Quadrandam.
Sed hoc opus hic labor est, data quadranda
Figura invenire quadratricem ejus aliquam.
i quodem temunsrata suala ests si secridum
figtt