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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
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b. TII.
ASTRONOMTA L H LSFCX
178
nibus Opticis altimetur: cujus faciendi modos duos propiu,
alterum facobi Grecorii Anno 1668 cditum, alterum Christiant
Fucenii in lua Cosmo-theoria traditum.
PROPOSTTIOLVTT. LEMMA.
Fusdem sphaerae illustrationes, in diversis à luciao corpore u
stantiis, sunt in reciproca duplicata ratione distantiarum.
Licet Propositio haec Facile ConsegUatUE CX PFOD. XEVTTI. L IB. I.
libet illam hic demonstrare. Sit a corporis lucidi punctum quod
vis ad libitum Cumptum; sitque BC Sphaera illustrata diameter ra
diis directe objecta, in minore distantia à lucido: By eadem dia-
meter in majore distantia: hoc CA, SIE A P radiuS adL CCnETUI F per.
tinsens ipsi Bc normalis, _ AC ip(I BY: TUNSAnEUr AB, AC, 8E prO.
ducta concurrant in D e F cum B7 etiam
producta. Centro a, distantid AD vel AF
describatur circuli arCUS DF, Cui AB, AC 8
AV producta occurrant in F, G CEK, COn-
cipiaturque Aigura hac super aXCM AC YO.
tata. Patet radios omnes in sphaera cujus
diameter Dc incidentes, illa ablata, in sphae-
ram cujus diameter cA DF Sparoi: e id00
illustratio sphaera, cujus diameter BC, est ad
illustrationem sphara, cujus diameter BY.
ut omnes radii intra sectorem sphaericum rotatione sectoris circula
ris ADC genitum contenti ad omnes radios intra sectorem sphaeri-
cum rotatione ipsius a C senitum contentos; hoc est, ut superfi.
cies Sphaerica rotatione arcis De producta ad superficiem sphaeri
cam rotatione arcis Er productam; hoc CA (PEF PrOP. XLIX. L iB. I.
Trehimed. de Sph. 5 CγV.) ut circulus radio Da ad circulum radio
HC, sire in duplicata ratione DC ad HC. Sed in parvis ansulis,
quales TupponimUS D AG _E HAC, DC est ad Fra quamproxime ut
De ad Bc: Ex ideo illurtratio sphaera, cujus centrum in F, est ad il.
lustrationem ejusdem vel xequalis sphaera, cujus centrum in c, in
duplicata ratione DE ad BC, SIVC DE ad DF, SIVO AC ad A F HOC CH,
in reciproca duplicata ratione distantiarum. Cumque idem pro-
Pter ealdem rationes verum sit de alio quoris lucidi corporis pun-
Eto aque ac de a, patet provotcum.
Similiter, ejusdem sphaera illustrationes ab aequalibus corporibus
lucidis inaegualiter distantibus tactae sunt in reciproca duplicata ra-
tione distantiarum à corporibus ictis lucidis.
EROPOSTTTO LVTIT LRMMA.
Mnes Racii Solares in Planetam unum incidentes sunt ad
omnes Racios Solares in Planetam alterum incidentes in du-
plicata ratione chordarum Parallarium Borizontalium Solis ex
Dlanetis istis sectati.
Reterat 5 Solis punctum quodris radians; a B, CD sphaera, qua
rum
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