Abbreviations

Introduction

The Principles of Cartesian Philosophy

Preface

Lodewijk Meyer

Part 1.

Prolegomenon.

Definitions

Axioms

Prop. 1: We cannot be absolutely certain of anything as long as we do not know that we exist.

Prop. 2: `I am' must be self-evident.

Prop. 3: `I am', insofar as the `I' is a thing consisting of body, is not a first principle and is not known through itself.

Prop 4: `I am' cannot be the first known principle except insofar as we think

Axioms taken from Descartes.

Prop. 5: The existence of God is known solely from the consideration of his nature.

Prop. 6: The existence of God is also proved a posteriori from the mere fact that the idea of him is in us.

Prop. 7: The existence of God is also proved from the fact that we ourselves exist while having the idea of him.

Prop. 8: Mind and body are distinct in reality.

Prop. 9: God is a supremely understanding being.

Prop. 10: Whatever perfection is found in God, is from God.

Prop. 11: There cannot be more than one God.

Prop. 12: All things that exist are preserved solely by the power of God.

Prop. 13: God is supremely truthful, and not at all a deceiver.

Prop. 14: Whatever we clearly and distinctly perceive is true.

Prop. 15: Error is not anything positive.

Prop. 16: God is incorporeal.

Prop. 17: God is a completely simple being

Prop. 18: God is immutable

Prop. 19: God is eternal.

Prop. 20: God has preordained all things from eternity.

Prop. 21: Substance extended in length, breadth, and depth exists in reality, and we are united to one part of it.

Part 2.

Postulate.

Definitions

Axioms

Prop. 1: Although hardness, weight and the other sensible qualities may be separated from a body, the nature of the body will nevertheless remain unimpaired.

Prop. 2: The nature of body or matter consists only in extension.

Prop. 3: That there should be a vacuum is a contradiction.

Prop. 4: One part of a body does not occupy more space at one time than at another; and, conversely, the same space does not contain more body at one time than at another.

Prop. 5: There are no atoms.

Prop. 6: Matter is indefinitely extended, and the matter of the heavens and the earth is one and the same.

Prop. 7: No body moves into the place of another body unless at the same time that other body moves into the place of another body.

Prop. 8: When a body moves into the place of another body, at the same moment of time the place quitted by it is occupied by another body immediately contiguous to it.

Prop. 9: If a circular tube ABC is full of water and is four times as wide at A as at B, then at the time that the water (or any other fluid body) at A begins to move toward B, the water at B will move at four times that speed.

Prop. 10: The fluid body that moves through the tube ABC (of Prop. 9) receives an indefinite number of degrees of speed.

Prop. 11: The matter that flows through the tube ABC (of Prop. 9) is divided into an indefinite number of particles.

Prop. 12: God is the principal cause of motion.

Prop. 13: God still preserves by his concurrence the same quantity of motion and rest that he originally gave to matter.

Prop. 14: Each single thing, insofar as it is simple and undivided and is considered only in itself, always perseveres in the same state, as far as in it lies.

Prop. 15: Every body in motion tends of itself to continue to move in a straight line, not in a curved line.

Prop. 16: Every body that moves in a circle (e.g., a stone in a sling) is continuously determined to continue in motion at a tangent to that circle.

Prop. 17: Every body that moves in a circle endeavors to move away from the center of the circle that it describes.

Prop. 18: If a body A moves toward a body B, which is at rest, and B loses nothing of its state of rest in spite of the impetus of body A, then neither will A lose anything of its motion, but will retain entirely the same quantity of motion that it had before.

Prop. 19: Motion, regarded in itself, is different from its determination toward a certain direction; and there is no need for a moving body to be for any time at rest in order that it may travel or be repelled in an opposite direction.

Prop. 20: If a body A collides with a body B and takes it along with it, A will lose as much of its motion as B acquires from A because of its collision with A.

Prop. 21: If a body A is twice as large as B and moves with equal speed, A will also have twice as much motion as B, or twice as much force for retaining a speed equal to B's.

Prop. 22: If a body A is equal to a body B, and A is moving at twice the speed of B, the force or motion in A will be twice that in B.

Prop. 23: When the modes of a body are compelled to undergo variation, that variation will always be the least that can be.

Prop. 24, Rule 1: If two bodies, A and B, should be completely equal and should move in a straight line toward each other with equal velocity, on colliding with each other they will both be reflected in the opposite direction with no loss of speed.

Prop. 25: Rule 2: If A and B are unequal in mass, B being greater than A, other conditions being as previously stated, then A alone will be reflected, and each will continue to move at the same speed.

Prop. 26: If A and B are unequal in mass and speed, B being twice the size of A and the motion in A being twice the speed of that in B, other conditions being as before stated, they will both be reflected in the opposite direction, each retaining the speed that it possessed.

Prop. 27, Rule 3: If A and B are equal in mass but B moves a little faster than A, not only will A be reflected in the opposite direction, but also B will transfer to A half the difference of their speeds, and both will proceed to move in the same direction, at the same speed.

Prop. 28, Rule 4: If a body A is completely at rest and is a little larger than B, with whatever speed B moves toward A it will never move A, but will be repelled by A in the opposite direction, retaining its original motion.

Prop. 29, Rule 5: If a body A at rest is smaller than B, then however slowly B moves toward A, it will move it along with it, transferring to it such a part of its motion that both bodies thereafter move at the same speed.

Prop. 30, Rule 6: If a body A at rest were exactly equal to a body B, which is moving toward it, to some degree A would be impelled by B, and to some degree B would be repelled by A in the opposite direction.

Prop. 31, Rule 7: If B and A are moving in the same direction, A more slowly and B following it more quickly so that it finally overtakes A, and if A is bigger than B, but B's excess of speed is greater than A's excess of magnitude, then B will transfe to A so much of its motion that both will thereafter move at the same speed in the same direction. But if, on the other hand, A's excess of magnitude should be greater than B's excess of speed B would be reflected by it in the opposite direction, retaining all its motion.

Prop. 32: If a body B is surrounded on all sides by particles in motion, which at the same time are impelling it with equal force in all directions, as long as no other cause occurs it will remain unmoved in the same place.

Prop. 33: Body B, under the conditions stated previously, can be moved in any direction by any additional force, however small.

Prop. 34: Body B, under the same conditions as previously, cannot move more quickly than it is impelled by the external force, even though the particles by which it is surrounded are in much swifter motion.

Prop. 35: When body B is thus moved by an external impulse, it receives the greatest part of its motion from the bodies by which it is constantly surrounded, and not from the external force.

Prop. 36: If any body (e.g., our hand) can move in any direction whatsoever with equal motion without offering any resistance to any bodies or meeting with any resistance from any other bodies, then in that space through which it would thus move there must necessarily be as many bodies moving in one direction as there are bodies moving in any other direction, their force of speed being equal to one another's and to that of the hand.

Prop. 37: If a body A can be moved in any direction whatsoever by any force, however small, it must necessarily be surrounded by bodies that are moving at the same speed as one another.

Part 3.

Postulate.

Definitions

Axioms

Prop. 1: The parts into which matter was first divided were not round but angular.

Prop. 2: The force that brought it about that the particles of matter should move about their own centers, at the same time brought it about that the angles of the particles should be worn away by collision with one another.

Metaphysical Thoughts

Part 1

Chap. 1: Of Real Being, Fictitious Being, and Being of Reason.

Chap. 2: What Essence is, what Existence is, what Idea is, and what Potency is.

Chap. 3: Concerning the Necessary, the Impossible, the Possible, and the Contingent.

Chap. 4: Of Duration and Time

Chap. 5: Of Opposition, Order, etc.

Chap. 6: Of the One, the True, and the Good.

Part 2

Chap. 1: Of God's Eternity.

Chap. 2: Of the Unity of God.

Chap. 3: Of the Immeasurableness of God.

Chap. 4: Of the Immutability of God.

Chap. 5: Of the Simplicity of God.

Chap. 6: Of the Life of God.

Chap. 7: Of God's Intellect.

Chap. 8: Of God's Will.

Chap. 9: Of God's Power.

Chap. 10: Of Creation.

Chap. 11: Of God's Concurrence

Chap. 12: Of the Human Mind.

Appendix 1: Cross-References of the PPC to the PPH.

Appendix 2: Meyer's Dissertation.

Introduction.

Dissertation.

Bibliography.

Latin and Dutch Editions.

Translations and Editions of PPC and CM.

Secondary Literature.