Printed in the United States of America
FOOTNOTES:
[1] Azure transparent spheres conceived by the ancients to surround the earth one within another, and to carry the heavenly bodies in their revolutions.
[2] Book I., Prop. i. The areas which revolving bodies describe by radii drawn to an immovable centre of force do lie in the same immovable planes and are proportional to the times in which they are described.
Prop. ii. Every body that moves in any curve line described in a plane and by a radius drawn to a point either immovable or moving forward with a uniform rectilinear motion describes about that point areas proportional to the times is urged by a centripetal force directed to that point.
Prop. iii. Every body that, by a radius drawn to another body, howsoever moved, describes areas about that centre proportional to the times is urged by a force compounded out of the centripetal force tending to that other body and of all the accelerative force by which that other body is impelled.
[3] If the periodic times are in the sesquiplicate ratio of the radii, and therefore the velocities reciprocally in the subduplicate ratio of the radii, the centripetal forces will be in the duplicate ratio of the radii inversely; and the converse.
[4] i.e., showing convexity when in such a position as that, to an observer on the earth, a line drawn between it and the sun would subtend an angle of 90° or thereabouts.
Transcriber Notes:
Variant spelling and punctuation have been preserved.
Image quality of the Frontispiece is poor.