## The Mathematical Principles of Natural Philosophy, Volume 1Isaac Newton's The Mathematical Principles of Natural Philosophy translated by Andrew Motte and published in two volumes in 1729 remains the first and only translation of Newton's Philosophia naturalis principia mathematica, which was first published in London in 1687. As the most famous work in the history of the physical sciences there is little need to summarize the contents.--J. Norman, 2006. |

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### Common terms and phrases

ABFD abfolute accelerative afcend alfo angle VCP apfides apfis arife axis becauſe bifected cafe caufes centre of force centre of gravity centripetal force circle common centre conic fection corpufcle curve line cycloid decreaſe defcend defcribed demonftrated diameter diftance diminished drawn duplicate ratio ellipfis equal fame ratio fcribe fecond feveral fhall fides figure fimilar fince firft firſt fituate focus folid fome force tending fphærical fphere fquare fubduplicate ratio fuch fuperficies fuppofe fyzygies given by pofition given points given ratio globe hyperbola immoveable increaſed infinitum interfections inverfely laft latus rectum lefs LEMMA let fall motion move ofcillations orbit paffing parabola parallel parallelogram particles perpendicular plane principal axe principal vertex prop proportional PROPOSITION quadratures quantity radius reafoning reciprocally rectangle refiftance reft right line ſpace tangent thefe themſelves THEOREM theſe thofe thoſe trajectory trapezium triangles velocity whofe

### Popular passages

Page 11 - Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

Page 62 - From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.

Page 34 - ... of a hammer) is (as far as I can perceive) certain and determined, and makes the bodies to return one from the other with a relative velocity, which is in a given ratio to that relative velocity with which they met.

Page 17 - The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

Page 39 - QUANTITIES, AND THE RATIOS OF QUANTITIES, WHICH IN ANY FINITE TIME CONVERGE CONTINUALLY TO EQUALITY, AND BEFORE THE END OF THAT TIME APPROACH NEARER THE ONE TO THE OTHER THAN BY ANY GIVEN DIFFERENCE, BECOME ULTIMATELY EQUAL.

Page 18 - If a body impinge upon another, and by its force change the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, towards the contrary part.

Page 13 - The effects which distinguish absolute from relative motion are the forces of receding from the axis of circular motion. For there are no such forces in a circular motion purely relative, but in a true and absolute circular motion they are greater or less, according to the quantity of the motion.

Page 11 - This force consists in the action only, and remains no longer in the body when the action is over. For a body maintains every new state it acquires, by its inertia only. But impressed forces are of different origins, as from percussion, from pressure, from centripetal force.

Page 11 - Therefore we may now more nearly behold the beauties of Nature, and entertain ourselves with the delightful contemplation; and, which is the best and most valuable fruit of philosophy, be thence incited the more profoundly to reverence and adore the great Maker and Lord of all.