"Algebra made an enormous difference to geometry. Whereas Archimedes had to make an ingenious new approach to each new figure... calculus dealt with a great variety of figures in the same way, via their equations. That was the whole point. Calculus was a method of calculating results, rather than proving them. If pressed, mathematicians could justify their calculations by the method of exhaustion, but it seemed impractical if not unnecessary... Huygens was probably the only major mathematician who stuck to the 'methods of the ancients.' The methods of calculus were so much more powerful and efficient that rigour became secondary. ...By the middle of the eighteenth century, calculus had solved almost all the problems of classical geometry, and new ones the ancients had not dreamed of. It had also revealed the secrets of the heavens, explaining the motions of the moons and planets with uncanny precision."