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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 236, page id 1040780814:0254
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2
ASTRONOML A PHYSFCA.
alsumpta isitur majore Are Orbita Terra (hre hujus semisse Tellu-
ris Distantia media a Sole) habebitur magnitudo Orbita Planeta:
penitus isitur determinatur Plancta Orbita. Et Tempus, quando
Planeta hic Aphelium tenebat, similiter determinatur, atque idem
in Planeta Tellare PrOD. XIV. Factum.
Ouoniam Orbitx Planetae Fllipricae Species Tola ex datis determi
NatUE, (UIE CX PFOD. XIV. ConStaL,) _ ejus Orbitx maonitudo respectu
Orbitx Terra ex comparatione Temporum periodicorum horum
Planetarum per praec. concluditur; idem poterit aliunde inserpi. Fa-
ciendo nempe ut Orbita certa Speciei (ex tribus Locis Centricis de
terminatae) ex Sole ut Umbilico deseripta, transeat per ipsum L0.
cum Planeta in linca Nodorum per Prop. XIX. hujus inventum:
Fioc namque punctum, in Planeta Orbita datum, tantundem valet
ad illius maonitudinem respectu maonitudinis Orbita Terrettris
determinandam, acque ejusdem Axis major supra definitus: TRius
enim puncti Distantia a Sole in partibus linearum Orbita Telluris
determinata cst; potestque alter horum modorum describendi Or-
Ditam per alterum examinari et corrigi.
Et hinc motus Apsidum cujutris Primarii definietur; nimirum
eodem modo quo prius Nodorum motus.
PROPOSEEIOZEVI LEMMA.
tis umbilico  lonsitudine axis majoris, describere Fllipsin
 per data duo puncta transeuntem.
Sit S Figurx describenda umbilicus, ae longitudo axis majoris, L
_  duo puncta per quae Flliplis trantire debet. Centro F distantia
aequali exceltui rectae ap supra rectam L. S describatur circuluS CF;
e timiliter centro  distantia aequali excellui rectae ar fupra 18
describatur circulus RF priorem secans in
F; exit F FMipseos describenda umbilicus
alter: TTisce isitur umbilicis S_ F, C aXC
majore aquali recta ap, descripta Fllips
erit ea qua quaeritur. Ouoniam enim L. F
aqualis CAt AP - LS, CrIt LS F L F aqualis
AP. Pari modo AP Xquatur IS F VF: Onde
(DeT PFOD. LIT. Lib. tert. Conicorum) Fllipsis umbilicis s d F de-
scripca, axem majorem habens aequalem recta aP, transibit per
puncta L. 8 l.
Facile es ex hujusmodi constructione Cicometrica calculi mo-
dum Altronomia accommodatum excositare. Fx datis enim tri
bus punctis s, L. _I, hoc eA, ex datis tribus lateribus trianguli ST. I.
innoteseunt anguli. RursuS, in triangulo L. IF dantur omnia latera;
nempe L. V uEpriuS, L. F ditterentia datarum rectarum AP _ L. S, e
IF disterentia iplarum aP, 15; innotescit isitur angulus FL. I: Sed
prius notus erat SLV, ergo dabitur angulus SI. F. In triangulo ie1
tur ST. F, Cdatis LS, L F Cum angulO SL. F innOteICet latuS S F dictan-
tia focorum, et ansulus L.SF inter L. S positione datam e axem
majorem;
1D. lLL
d