Newton had completed the first draught of the work by the end of 1685, though none of it was Bent till April, 1GSG. The third book was presented to the Society, April 6, 1687, in proof, probably, since the whole was published (at ten or twelve shillings a copy) about Mid summer, 1687. The order of the Council of the Society to license the book was made on June 20, 1686, and the imprimatur of Pepys was dated July 5.
The part which Halley had in the matter would alone immortalise his name. Ile found out the ability of Newton to write such a work, prevailed upon him to write it, took charge of the publication, pre vented the author from materially mutilating it in disgust, paid the expenses of printing, at a time when, owing to his father's death and consequent litigation, he had nothing to spare (which never happened to him before or after), gave a copious explanation of it in the Philoso phical Transactions, and is generally admitted to have been for a long time the only person in Europe who showed that he thoroughly appreciated the value of the work, and knew the place it must occupy in the history of discovery.
The interest attached to the second and third editions of the Prineipia (superintended by Cotes in 1713, and by Pemberton in 1726) is considerable, with reference to the alterations made in them by Newton. It would not however be worth while to specify these alterations, which are numerous, some in correction of errors, others in extension of views. With reference to the suppression of tho celebrated Scholium, see CO]MERCIUM Ertsrottcen and FtextoNs.
The Principle of Newton contains the dedication to the Royal Society, a short preface, verses by Halley in honour of Newton, defi nitions, axioms, a first book on untwisted motion, a second on resisted motion, and a third on the system of the universe. Halley's;
verses were somewhat altered by Bentley in the second edition, but the original readings were very nearly restored in the third. Newton wrote a short preface for each of the editions, and Cotes one of con siderable length for the second. The dates of the Newtonian prefaces are, May S, 1686; March 28,1713; January 12,1725-6. The following is the description of the contenta of the third edition : The definitions comprise, 1. Qunntity of matter measured by density and volume jointly. 2. Quantity of motion [MOMENTUM] by velocity and quantity of matter jointly. 3. Via insita, or'via inerthe. [Benne.] 4. Vie impresea, or external force. 5. Centripetal force. 6. Absolute magnitude of centripetal force. 7. Accelerating force. 8. Moving force. A !scholium is added on 'time, space, and motion, the latter considered absolutely and rotatively.
The axioms are the three laws of motion [MOTION, LAWS or] and certain corollaries, namely :-1. The composition of velocities and forces. 2. Their resolution, and deduction of the property of the lever. 3. Momentum of a system in a given direction not changed by the mutual action of the parts. 4. Nor the motion of the centre of gravity. 5. Relative motion of bodies not altered by absolute motion of tho space they move in. 8. Nor by equal and punliel accelerating forces applied to alL A scholium is added, containing the experimental verifications of the third law iu the cases of impact, attraction, and operation of machines.