The tangents of the angles of a sector of a circle and of a hyperbola, 1687.

Proposition 9, Theorem 7, concerning the motion of bodies that are resisted as the squares of the velocities, from the first edition of Newton's 'Principia Mathematica' (1687): 'Given what has already been proved, I say that if the tangents of the angles of a sector of a circle and of a hyperbola are taken proportional to the velocities, the radius being of the proper magnitude, the whole time of ascending to the highest place will be as the sector of the circle, and the whole time of descending from the highest place will be as the sector of the hyperbola.' The discoveries of English physicist and mathematician Isaac Newton (1642-1727) were prolific and hugely influential on science and thought.