Newton's Principia ignited the Scientific Revolution, but the work-sheets and sketches showing how he composed his masterpiece have been lost. Fortunately, he left behind enough clues that make it possible to give a plausible reconstruction how he made his discoveries. Surprisingly, such a reconstruction has not been attempted before. In the winter of 1679, Robert Hooke initiated a correspondence with Newton outlining the physics of planetary motion. But Hooke was unable to formulate his concepts in mathematical form, and afterwards Newton accomplished this formulation giving a geometrical expression for the passage of time, thus laying the foundation for the Principia. On Dec 10, 1684, four months after a visit of Edmond Halley, Newton sent the first manuscript for his book to the London Royal Society, "designedly abstruse to be understood only by able Mathematicians". I will show, however, that with simply a pencil and a ruler, and without Calculus, good approximations of orbits for central forces can be obtained graphically, which also clarifies the content of the Principia.