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The Mathematical Principlesof Natural Philosophy

Philosophiæ Naturalis Principia Mathematica

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The book that founded physics. Its opening chapter defines mass, momentum and force, and asks what it means to move at all: absolute and relative time, space and motion, with the spinning bucket and the two globes on a cord.

This is a sample: 1 of 5 chapters.

From the lectures

A car seat with a phone and a bag: while the car brakes, the phone's accelerometer trace jumps and the bag slides forward although nothing pushes it.
How Much Matter, How Much Motion

The Bag Keeps Going

Put your phone flat on the passenger seat of a car and open any free sensor app that shows the accelerometer. While the car rolls steadily along a straight road, the reading in the direction of travel stays close to zero.

A person on a bathroom scale that pushes up as hard as gravity pulls down; below, F equals m a and W equals m g, and the pull on a whole body as the sum of pulls on its parts.
Three Ways to Measure One Pull

Weight Is Mass Times g

The third is the motive quantity: a measure proportional to the motion, the momentum, that the pull produces in a given time.

A fixed grid of true space with a box of air on the Earth carried across it; below, a cube and a flat slab of equal size filling equal places.
True Time, True Space, and the Sailor

True Space and Places

Then space. Absolute space, of its own nature, stays always the same and never moves. Relative space is a movable measure of it, fixed by the senses through its position among bodies, such as the space under the ground, the air, or the sky, measured from the earth.

A row of bars for the lengths of natural days, slightly different from one another, against a dashed line for the even day of true time, with corrections and a pendulum clock and Jupiter's moons as checks.
True Time, True Space, and the Sailor

Natural Days Are Unequal

Back to time, where astronomy draws the line in practice. Absolute time is separated from relative time by the equation, or correction, of common time.

Two rows of two boxes, A and B: pushing only B changes their relative motion though A is untouched; pushing both equally keeps their relative position though both truly move.
Why True Motion Cannot Be Read from Neighbours

Push the Other Body

Then come the causes. What separates true from relative motion is force impressed on a body. True motion is never created or changed except by a force pressed on the body itself.

Two columns: the quantities themselves (time, space, place, motion) on the left and their visible measures (clock, room, position, change against bodies) on the right, with an arrow from each measure to what it measures.
The Bucket, the Two Globes and the Purpose of the Book

Quantities and Their Measures

From all this Newton draws a lesson about words. Relative quantities are not the quantities whose names they carry, but the visible measures of them, accurate or not, which people commonly use instead.

How it was made

Examples for: a curious adult with school physics who uses a smartphone every day; add one modern instance per idea, such as GPS satellites, a phone's accelerometer or a car braking

The source

The lectures retell the English text of Project Gutenberg #76404, Andrew Motte's translation (first American edition, 1846). The author died in 1727; the work is in the public domain. The retelling, the drawings and the voice are made by AI and checked against the book by a second model; nothing was edited by hand. How AI is used.

The lectures are free to read, share and quote with a link to this page.

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