/ Research / Newton / Principia Mathematica Simplified / The Laws of Motion / Corollaries 1-2

Corollaries 1-2

by Isaac Newton Icon

Table of contents

Corollary 1

A body that is moved by two perpendicular forces will move in a diagonal

Force on a plane

A force M impressed on a body at A will be uniformly carried from A to B.
A force N impressed at A will be carried from A to C.
If N and M act together, their forces will an the same time be carried in the diagonal from A to D.
- Law 2 means that N will not at all change the velocity generated by M
- The body therefore will arrive at the line BD in the same time, whether the force N be impressed or not. Therefore at the end of that time, it will be found somewhere in the line BD.
Likewise, it will be found somewhere in the line CD at the end of the same time, if N were impressed. Therefore, it will be in the point D where both lines meet.
- But Law 1 means that it will move from A to D.

Thus, a single force AD is made up of two forces AC and CD just as those two forces can arise from AD.

Center O has 2 unequal radii OM and ON. M sustains a weight A through a cord MA. N sustains a weight P by the cord NP…