c 518 ] 
gle FEH equal to the given angle F A H. There- 
fore the whole figure E H F D is given in fpecies, 
and confequently the angle A D E, as before. 
In the laft place fuppofe a circle to circumfcribe 
r-. the triangle, and interfedt one of the lines, 
^ 2I ’ as AC, in I. Here DI being drawn, 
tlie angle DIF will be equal to the given angle 
D E F in the triangle ; confequently D I is inclined 
to AC in a given angle, and is given in pofition, 
as alfo the point I given ; whence I E being drawn, 
the angle FIE will be the complement of the angle 
E D F in the triangle to two right. Therefore I E 
is given in pofition, and by its interfedtion with the 
line A B gives the point E, with the pofition of 
DE, and thence the whole triangle, as before. 
Here it may be obferved, that the angle D of 
the triangle EDF given in fpecies touching a given 
point D, and another of its angles touching AC, the 
line I E here found is the locus of the third an- 
gle E. 
Again, in the agronomical lectures of Dr. Keil, it 
is propofed to find the place of the earth in the eclip- 
tic, whence a planet in any given point of its orbit 
{hall appear flationary in longitude, and a folution 
is given from the late eminent aflronomer, Dr. Hal- 
ley, upon the affumption, that the orbit of the earth 
be confidered as a circle concentric to the Sun. 
But for a compleat folution of this problem let the 
following lemma be premifed. 
The velocity of a planet in longitude bears to the 
velocity of the earth the ratio, which is compounded 
of the fubduplicate ratio of the latus re Slum of the 
greater axis of the planet’s orbit to the latus reflum 
of 
