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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 47, page id 1040780814:0065
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Tib. 1
duplum
RX 5PG
5)
C deimon
ad quoc
eta, 9
lius pet
Vis hac
impressa
sit reCI
retert
uneentt
Fillip)
POdcu
Apol
H, PH
ilu
Dud
PRO
eE CTFOMETETCA LBLMENEA.
eRoPoStTIO La
Fvolvatur corpuo in F quaeritior
Tendentis ad Focum F. llipsis
Sit FIIipS A P M, cujus perimeter d CpOre revolvente describi-
tur; hujus focus sire umbilicus alter s, ad quem dirisitur Vis qud
corpus a mocu rectilineo retractum in Orbita F. Iliptica recinetur:
Ouxritur hujus Lex.
Ducantur KIlipsis axes conjugati LA, C L, I centro c se invicem
decustantes. Ft per quodlibet in ejus perimetro punctum e ducan
tur recta ez Fllipsin contingens, e diameter P M, X huic conjugata
TCK ad P Z Parallela, ad quam ex e demittatur normalis P N. Com-
pleatur parallelosrammum PCrH; rectaque Te F.Niplin continset per
XVII. Lib. T. Conic. Sungatur Se secans lR  P. Per B ips P prOxi
mum ducantur BR ad P S, 8
BX ad PZ Parallela, rCCtX SP
IN X, _E MD IN O OCCUETONS.
Vis centripeta ad s tendens
CA (DEF PFOD. ZZXVIT.) rC
ciproce ut Solidum SP ZuBD
Hoc proinde ex FIlipsiS na-
tura est computandum. In
quem tinem FNip(IS Latus
Rectum Principale, sive ad
axem majorem T A perEI-
nens, rocetur L. Ratio ipsiuIS
L XBR ad BDg componitur
exrationibus L = BR ad L X P O, LXPO ad M OKPO, MO= PO ad BOG.
BOg ad BXG, _ BXG ad BDg: Sed ratiO ipHIUS L XBR ad L XPO,
sive (per PCop. T. FI. 6) ipsius BR aut P X ad P0, aequalis es rationi
DE ad PC, (per PrOP. II. FL. 6,) quia XO est paraIlela E C; _ (per
Draced.) PE aequalis a c: Frso ratio ipsius L = B R ad L x P0 aequalis
eAt rationi AC ad P C. POrTO, ratio LXP O ad MON PO est eadem
cum ratione F ad NO. Ft ratio ip(IUS AT OLPO, SIVO MOD rectan-
suli, ad Bog eadem cAt (Per XXI. Lib. T. Conic.) cum ratione
rectanguli MCP (hoC CA CP9) ad TC9. FL, in casu praesenti, ratio
B09 ad BXg eA ratio aequalitatis; nam, cocunte puncto B CUM P.
B0 Tt ipsi B X aequalis. Denique, ratio B Xg ad eDq aequalis est ra
tioni e Eg ad PNg: (Priangula enim BDX, PN P. sunt xquiansula,
ob angulos ad D e N rectos; _ BXD, PF N alternos in duabuS Par-
allelis B X, F N itidem aequales.) FF P Fg est aequale c A9, quia
iP(X reCta (peF PrX CCd.) aequantur: Frso racio BXq ad BDg eadem
CA cum ratIONC CAg ad P HG. POTKO, (Per PrOp. LZXII. Lib. 4.
Crecorii a So. Vincentio, rectansulum Tub cC e c a aequale eAt
parallelosrammo P CFI; hoc CA, rectangulo SUD LC X P N: Ouare
Dex
it
Ten Vis cencrixeta