Principia: Sections I, II, III

AB² accelerating effect action angular velocity apse arcs described axes bisect body describes body moves center of force center of gravity central orbit centripetal force chord of curvature circle of curvature circular conic section conjugate diameters constant curve cycloid diameter of curvature duplicate ratio ellipse equiangular spiral extremities finite curvature fixed point focus force varies given point hence hyperbola impulse indefinitely diminished intersect latus rectum Lemma locus magnitude major axis orbit described ordinate parabola parallel parallelograms particle perpendicular plane polygon position PROP proposition prove quantities radius of curvature ratio of equality represented right angles SCHOLIUM shew similar space described square straight line string subtense supposed tangent third proportional triangle ultimate ratio uniform velocity vanishes varies inversely vertex