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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 430, page id 1040780814:0448
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ib. Y
ASTRONOMLA PAYSTCE
1B
circularis (hoc est, quadrato semistis ;=) ad circuli diametrum sive
LN
25R applicato; hoc eAt, quadrato Y= applicato ad 25R, sire
AMg
ASR. Spatium isitur per quod corpus e quiete ex altitudine es de-
miltum cadendo percurrit, semisse temporis quo Cometa arcum Par.
abolicum av B describat, xquale est A Mg
+SR. Sed (per PFOP. XL. H. L ib
T.) vis centripeta sire graritas acceleratrix versus Solem ad distan-
tiam SF. est ad graritatem acceleratricem rersus cundem ad distan-
tiam SR UE SRG ad SL g; hoc CA, ob proportionaleS SR, SE, SV, WE
SE ad SV: FF igitur cum Cometa motu omni priratus de ex R de
mistus, semisse temporis quo arcum Parabolicum ar B describat,
AMq
cadat versus solem per spatium aquale  Su; idem pari tempore
ex L Similiter demistus cadendo vertus Solem percurret spatium
AMq
quod est 24.
Mq
Sy. POr-
r0, ex Parabola natura 4. SV eA lacus rectum diametri VM;
hoc est, rectansulum sub 4. 5V ec vm aequale est quadrato ipsius
2M
am, ideoque qSr ipsirmrecta est aequalis: Cometa isitur motu omni
privatus e demistus de altitudine L. S ut vertus Solems cadlat, A V
acceleratrice sire graritate, uniformi urgeatur aequali illi qud in
dicta altitudine sr. ursebatur, Pemisse temporis quo arcum P’arabo
licum are deseribat, cadet per rectam recta rm aequalem. O. P. D.
PROPOSTTIO ZZTT. LEMMA.
Tex puncto S, Parabolae AVB foco e Circuli et = centro, aucan-
tur aequales rectae Sr e st, ducantur item rectae AB, FF, Chor
dae arcuum quorum verticesr e t, secantes rectas sV, st in punctis
De∞ N, ita ut vD e +N sint aequales e admodum parvae respect
rectarum 5V C St; erit chorda aB ad diametrum quadrati, cujus
latus est chorda rc, in sub duplicata ratione rectae st ad sD rectam.
Per Y duCatuT VMt Parabola axi parallela, ChOTdR OCCUETENS IN
M, quaqUe (PeT PrOP. XLVI. L ib. J. Conic.) erit segmenti ar e diametel
cujus parameter es quadrupla rectae SV.
adCOquC AMQ = 4SVXVM. Cumque sII
(DeT PrOP. XXXV. BL. HIT.) TNG =+S F SNXt X
(quia SF =SN) 2SFxF N; exIt AMg: 4 5V
YM:: TNG: 25FF N, ideoque (Tumendo an
cecedentium quadrupla e permutando) c
rit ABG: YTG:: 4 SVXVM: 2SFxF N. SeC
(per oltensa in demonstratione PrOP. XV.
Ym = VD, _ ex hypoth. YD = +N; appli
cando isitur praecedentis analozia tertium terminum ad vit a
quartum ad TN, erit AB9: Y29:: 4. SV: 25t: hOC CA (PFOPteF Si
_St ex hypochesi aquales) ABg: FF9: : 25t: SV; id cAt, Ut 25+ ac
SV sire SD: _ duplicando consequentes, ABg: 2 L FFG : : 2 5t: 25D;
hOC