Table. 1.

Brief description of hypotheses and some propositions of ⟨On the motion of bodies in an orbit⟩.

Brief description
Hypothesis 1 In the first 9 propositions, resistance is assumed nil
Hypothesis 2 By its intrinsic force, an object progress uniformly in a straight line
Hypothesis 3 Forces combine by a parallelogram rule.
Hypothesis 4 In an effect of centripetal force, the distance is proportional to the square of the time.
Theorem 1 an orbiting body sweeps out equal areas in equal times
Theorem 2 the centripetal force is proportional to the square of the arc-length traversed, and inversely proportional to the radius.
Theorem 3 the centripetal force in a non-circular orbit is proportional to QRSP2×QT2
Problem 3 the centripetal force to produce elliptical orbit would be inversely proportional to the square of the distance
Theorem 4 Supposing that the centripetal force be reciprocally proportional to the square of the distance from the center, the squares of the periodic times in ellipses are as the cubes of their transverse axes.
Problem 4 for the case of an inverse-square law of centripetal force, initial conditions determine the shape of the orbit (ellipse, parabola, hyperbola)
New Phys.: Sae Mulli 2022;72:795~805 https://doi.org/10.3938/NPSM.72.795