# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/824573315:0261
# Permalink to this reading: https://leibnizlegible.com/page/824573315:0261?run=74
# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
# Folio 49, page id 824573315:0261
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=824573315&page=261
# Source image: https://digitale-sammlungen.gwlb.de/content/824573315/jpgs/default/00000261.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.93
# 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: the recognised lines in reading order, one per line.

Arithmetica insinitorum.
Cum enim Parabole, et Paraboloidum illorum plana sine
Peries rectarum in ratione sublecundanorum, Tubcercianorum,
Lubquarcanorum, suibquintanorum, _C. sire ucradices quadei.
dicae, cubiex, biquadraricae, Turdelolida, _c. Primanorum:
Cionoidea e Paraboloidea sic apcaca, Cune Peries planorum in du-
Plicaca racione iltarum rectarum; de propeerea, uc radices qua-
dracicae, cubicx, biguadracica, surdesolida 8c. Secundanorum.
quibus in cabella allignancur raciones illa 2 2d 4, 3 2d5, 4ad
6, 52d7, _C.
PROP. LXI. Corollarium.
Ed e hinc innotescit methodus quadrandi non
modo Parabolam sed e Paraboloidea omnia (eo-
rumqu complementa) non modo eagnorum ordina-
tim-applicatae procedunt juxta rationem simplicis alicu
jus potestatis, (de quibus dictum est prop. 55, 56, 57.
item prop. 23, 45.) Sed e juxtarationem potestatis cu-
jusvis ex simplicibus compositae. enta; si ordinatim- ap-
plicata sint in diametrorum ratione duplicata subtripli-
cata, subquintaplicata, sub septuplicata. exc. vel triplica.
ta subquadruplicata, subquintuplicata, ec. rationem
habebunt ad Paralleloerammum circum seriptum eam
quam habent 3 ad 5, 5 ad 7, 7 ad 9, 8 c. 4 adt Z. 5 ad
8, e c. Et eorum complementa (quorum ordinatim- appli-
catae erunt propterea in suarum diametrorum ratione sub-
duplicatae triplicata, quintuplicata, septuplicata, ec.
item subtriplicatae quadruplicata, quintuplicata,  c.
rationem habebunt 2 ad 5, 2 ad 7, 2 ad 9, 8 c. 3 ad 7.
3ad8, Cc. Pt siniliter in caeteris: juxta tenorem prae-
cedentis Tabella, prop. 59.
Nam s ordinatim applicaca sine in dismetrorum (IRrUIM
racione duplicaex subcriplicata, eric planum il lud series recta
rum que se hrabene ad inricem in quadraca radicum cubicarum
ret iadices cubicae quadratorum) numerorum arichmecice
PrOPOE.
CFOD.
61