# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1040780814:0440
# Permalink to this reading: https://leibnizlegible.com/page/1040780814:0440?run=74
# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 422, page id 1040780814:0440
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1040780814&page=440
# Source image: https://digitale-sammlungen.gwlb.de/content/1040780814/jpgs/default/00000440.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.92
# 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.

Lib. V
22
LESTRONOMLA PAZSTCAE
CiOROLLARTOM T.
Elinc sequitur in eadem Parabola ese rC in ratione lubdupsicata
iptius FA, Tire esse hanc FC ad aliam quamris Fe in subduplicata
ratione hujus pa ad alteram ra dicta alteri PC consruam: Nam
cum vr constans sit _ invariata, erit Feq ut ipsa FA, ideoque ipta
FC recta in subduplicata ratione rectae F A.
CiOROL L ARTUM 2.
Si in FV produeta capiatur V e aequalis VF, _ agatur infinita H H
ad re parallela, in quam ex quoris Parabola puncto a demitta
tur normalis AK; erit haec aequalis Pa distantia puncti a d Foco.
Ft econversosi ax, normalis ab a in _x rectam, aequalis fuerit recta
AF; erit punctum a ad Parabolam supra deseriptam, cujus focuS Y
C Vertex V.
Primum hinc patet quod Br aequalis sIE VD (per PrOP. XXXIHI. Lib.
T. Conic.) e AV per constructionem aequalis VF, _ ideo BF aequalis
HD: Sed prius ostensa cA A F aequaliS BF, _ PeF (PrOP. XXXIV. FL. I.)
KA IpSIED aequalis; unde R A dE F A XQUaNtUT.
Secundum vero hinc: ex hypothesi aK aequalis CA A F, quarO
punctum a est in recta perpendiculari ad junctam FK ex princto
ejus medio excitata. Si jam Parabola vertice v e foco F descri
Pta non transeat per a, transeat per aliud quodris recta xa (ejutre
productae) punctum, putaa: quare (per TuPra OstenSa) Fa XequaliS
eAt xa; unde punctum a est in pradicta perpendiculari ad FK CX
ejus puncto medio excitata. Dicta igitur perpendicularis occurret
recta xa in duobus punctis a e a, quod est ablurdum; Parabola
isitur focoF _ verricer deseripta transibit per a, PI fuerit A K X qua
IIS AF.
PROPOSEETOXV.
Icorpus moveatur in Parabola, (dum urcetur à viribus a
Parabolae focum tendentibus, quae sunt quadrato distantiae
foco reciproce proportionales,) ejus velocitas in quovis P araibolae pun
Eto est reciproce in sub duplicata ratione distantiae à Parabolae foco.
Sit De Trajectoria corporis Parabolica, cujus focus est s: Patel
(Cx COrOl. 2. PrOP. XET. T ID. 1.) ejus reloci.
tatem in princto celte reciproco ut SR per-
Dendiculum a focos in rectam cF tansen-
tem Parabolam inc, sire velocitatem COr-
Poris in c esse ad ejusdem relocitatem in
C ut Se ad SF: Sed (ex COrOl. T. PFOD.
PraeC.) SC CA ad SF in subduplicata rati
onc recta se adrectam sc; et igitur velo
citas corporis in c est ad eius velocitatem
in c in subduplicata ratione rectae Sc ad
rectam se; hoc est, corporis velocitas est
inverle in subduplicata rationo ejus di-
Hantiae a toco. O. F. D.