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X. Solution of Kepler’s Problem, by 
J. Machin, Ajlr. 'Prof. Grefli. and Seer. 
R. S. 
n 
M ANY Attempts have been made at different 
times, but, if I miftake not, never any yet 
with tolerable Succefs, towards the Solution of the 
Problem propofed by Kepler : To divide the Area of 
a Semicircle into given Parts, by a Line from a given 
Point of the Diameter, in order to find an univerfal 
Rule for the Motion of a Body in an Elliptic Orbit, 
For among the feveral Methods offered, fome are 
only true in Speculation, but are really of no Service. 
Others are not different from his own, which he 
judged improper : And as to the reft, they are all fome 
way or other fo limited and confined to particular 
Conditions and Circurnftances, as ftill to leave the 
Problem in general untouched. To be more parti- 
culars it is evident, that all Conftru&ions by Mecha- 
nical Curves are feeming Solutions only, but in 
reality unapplicable j that the Roots of infinite Se- 
ries's are, upon account of their known Limitations- 
in all refpeds, fo far from affording an Appearance of 
being fufficient Rules, that they cannot well be fup- 
pofed as offered for any thing more than .Exercifes in 
a Method of Calculation. And then, as to the uni- 
verfal Method, which proceeds by a continued Cor- 
reftion of the Errors of a falfe Fofttion,it is, when 
duly confidered, no Method of Solution at all in itfelfs 
becaufe, unlefs there be fome antecedent Rule or 
Hypothefis to begin the Operation, (as fuppofe that of 
an i 
