a 
om Review of the Principia of Newton, 
‘and his successors, so as to present an entire development 
by deductions directly from his assigned causes, of all the 
motions and phenomena of the great bodies of the universe. 
Astronomy is now made perfect in theory, and nearly so in 
every thing which relates to practice. It will be our busi- 
ness to point out the steps which have been taken in the 
Principia towards the accomplishment of that great object. 
the combination of mathematical with the physical 
principles of Newton, the invention of the orbit, or trajec- 
tory of a new planet, or comet, to all that degree of accu- 
racy which is attainable by approximating methods, may be 
considered as complete, so as to ascertain their motions from 
a few observations during the whole period of the former, or 
visible appearance of the latter. ‘This is by-far the pes 
advance ever made in Astronomy. ‘The 4th and 5 
tions of the Principia now under consideration, appear to 
have been the 3-4 ase ats of our author towards this great 
have e been superseded 
in his other works, and a the methods of Boscovitch, Tem- 
plehoff, Le Place, &c. We would only remark, that the 
20th and 21st Lemmas relate to a method of describing the 
conic sections by the revolution of angles about given points, 
and hep seeh pemniple- bm bechaatince on by succeeding ma- 
tou eotentace Maclaurin, in his Geémetria Organica, 
mi has ee ae it to numerous curves of the higher or- 
The next, or the 6th Section, is short, but not unimpor- 
tant. Assuming the Laws of Kepler, as demonstrated ex- 
perimentally and mathematically, they constitute a ceftain 
basis for an analysis of that which has been one of the great- 
among astronomers of the two last centuries, 
of | 
a Parabola, or Hy perbola, can scarcely be foundi in any of the 
the earth, and the comets must move in Ellipses, unless. urged 
by a force such as would cause their velocities to be equal to, 
or greater than that due to an — height, it is nevertheless 
ote use-in Astronomy to able to calculate the angu- 
me St fe belly iy moving in a parabola, as this figure 
excentric ellipses, and 
is: mie limit approximates so 
