# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0089
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0089?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 55, page id 1041163592:0089
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=89
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000089.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 27 lines, status machine
# Lines: 27 recognised, mean confidence 0.91
# 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.

RINCIPTA MATHEMALICA.
PX DF ut arca dato cempore descripta, le cus pel 
un subduplicata racione laceris recti.
 l
P RIMVC.
et
Corol. L. Latera recta principalia lune in ratione compolica ex
duplicata ratione perpendiculorum ee duplicata ratione veloci-
tatum.
Corol. 2. Velocitates corporum in mavimis et minimis ab umbi-
lico communi distantiis, sune in ratione composita ex ratione di-
stantiarum inverse sc subduplicata ratione laterum rectorum princi-
palium directe. Nam perpendicula jam sunt ipEx distantiae.
Corol. 3. Idcoque velociras in Conica sectione, in maxima vel
minima ab umbilico distantia, est ad velocitatem in C’irculo in ca-
dem a centro distantia, in Cubduplicata ratione laceris recti princi-
Dalis ad duplam illam distantiam.
Corol. 4. Corporum in Ellipsibus Srrancium velocitates in medi-
ocribus distantiis ab umbilico communi (unt cadem quae corporum
errancium in Circulis ad casdem distantias; hoc est (per. C orol 6.
ErOp. IV.) reciproce in subduplicata ratione distantiarum. Nam
Derpendicula jam sune Cemi-axes minores; ex hi sunt ut mediae
proportionales incer distantias ex latera recta. Componatur haec
ratio inverse cum subduplicata ratione lacerum rectorum directe, et
tiet rario subduplicaca distantiarum inverse.
orob. 5. In eadem figuras rel etiam in figuris diversis, quarum
latera