t i6 7 ] 
tains 10000 : The Angles BEI and BEG, being 
found by Methods commonly known, GE! their 
Sum or Difference will be likewife given. Alio Ex 
and Eft will be Sines of the Sun’s Altitude at the 
Beginning and End of thcEciipfe refpeflively ; IEx 
and IE[3 are the Angles at the Sun between the 
Vertex of the Place and the Pole of thofe Times; 
which being found, the Angle aE/ 3, their Difference 
will be known, from whence the Line afi and the 
Angle Ex\ 2 may be computed. 
The Angle GEx is the Sum or Difference of the 
known Angles GEI and IEx : In the Figure before 
us, the Complement of this to a Semicircle is Exy i 
Which being fubtra&ed from Ea/ 3 leaves the Angle 
yx/2 , from whence and the Line a/3, ay, and y{3 = 
may be found. _ — . 
Let a—S'e — b=xl=(3t, C—ay , and x—{3>r]=y^. 
Then V bb — xx=»e,and V bb — cc — 2 cx- t —xx=S'£, 
by Enel. 147 . ______ _ _____ 
Confequentiy^ — \/ d — xx=V bb — cc — icx=xx 
which being reduced, gives us the quadratic Equation 
xx *-{- cx = This Equation folved. 
gives us the Value of x , from which and ve will 
be likewife had. In the Triangle a£0 we have 
and the Angle ^a^=GEB given, whence a 0 and £9 
may be found : Confequently J9 will be known; 
and from the obferved Time of the Beginning of 
the Eclipfe, and hourly Motion of the Moon from 
the Sun, the Time when the Centre of the Shade 
is at 6 will be had. Laftly, in the Triangle Eia , 
We have given the Side Ea, and the Angle j£cti = 
BEx 
