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the velocity of the planet in longitude is to the ve- 
locity in its orbit in the ratio compounded of that of 
tire coline or the inclination of the planet’s orbit to 
the radius, and that of AK to AL. 
Moreover the ratio of the velocity of the planet in 
B to the velocity of the earth in any point of its or- 
bit is compounded of the fubduplicate of the ratio 
of the laius re Slum of the greater axis of the planet’s 
01 bit to the latus reffium of the greater axis of the 
taiths orbit, and of the ratio of the perpendicular 
le t fall from the lun on the tangent of the earth’s or- 
bit at the earth to AK, the perpendicular let fall on 
the tangent of the planet’s orbit at B. Therefore 
the velocity of the planet in longitude, when in B, 
to the velocity of the earth in any point of it’s orbit 
is compounded of the fubduplicate ratio of the latus 
rechim of the greater axis of the planet’s orbit, to the 
uiius re Hum of the greater axis of the earth’s orbit, of 
the ratio of the co-line of the inclination of the pla- 
net s orbit to the radius, and of the ratio of the lore- 
laid perpendicular on the tangent of the earth’s orbit 
to A L, the perpendicular on D I : thefe perpendi- 
culars being in the fame ratio with any lines drawn 
in equal angles to the refpedfive tangents. 
This being premifed, the place of a planet in the 
ecliptic being given, the place of the earth, whence 
the planet would appear hationary in longitude, may 
be aihgned thus. 
A denoting the fun, let B be a given place of any pla- 
net in it s orbit projected orthographically on the plane 
T>. 23. the ecliptic, CB the tangent to the pla- 
net’s projected orbit at the point B, which 
will therefore be given in pofition. All'o let DE be 
the 
