C tit ) 
When a Body deferibes any Traje&ory in a Void ot 
in a Medium, by a Force directed to One given Centre* 
the Velocity at any Point of the Traje&ory is to the 
Velocity by which a Circle could be deferibed in a 
Void about the fame Centre* at the fame Pittance, by 
the fame Gravity, in the fubduplicate Ratio of the 
angular Motion of the Ray drawn always from the 
Body to the Centre, to the angular Motion of the 
Tangent of the Traje&ory: And, if there be no Re- 
fiftance, the Velocity in the Traje&ory at any Point, 
is the fame that would be acquired by the Body, if it 
was to fall from that Point through One-fourth of 
the Chord of the Circle of Curvature that is in the 
Dire&ion of the Gravity, and the Gravity at that 
Point was to be continued uniformly during its 
Defcent, 
If the centripetal Force be inverfely as any Power 
of the Pittance whofe Exponent is any Number m 
greater than Unit, there is a certain Velocity (viz- . 
that which is to the Velocity in a Circle at the fame 
Pittance as V2 to V 1) which would be juft fuf- 
ficient to carry off the Body upwards in a vertical 
Line, fo as that it fhould continue to afeend for ever, 
and never return towards the Centre. If the Body 
be projected in any other Pire&ion with the fame 
Velocity, it will deferibe a Traje&ory which is here 
conftrudted : It is a Rarahola when m—i> a Logar- 
ithmic Spiral when m==. 3, an Epicyloidwhen 4, 
a Circle that paffes through the Centre of the Forces 
when m=z$j and the Lemnifcata when In 
general, it is conftru&ed by drawing a Perpendicular 
from the Centre of the Forces to a right Line given 
inPofuion, and any other Ray to the fame right Line, 
