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Page 53 - Laws of Motion I. Every body continues in its state of rest or of uniform motion in a straight line except in so far as it may be compelled by impressed force to change that state.
Page 32 - A POSTULATE is a self-evident problem ; such as, — 1. That a straight line may be drawn from one point to another. 2. That a straight line may be produced to any length. 3. That a straight line may be drawn through a given point parallel to another straight line.
Page 64 - We know that by the law of gravitation, the force with which one body attracts another varies directly as its mass, and inversely as the square of its distance...
Page 36 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 291 - ... figure ; (which is far the most natural and clear of all, as to this alone Aristotle's dictum may be at once applied.) In the second figure the middle term is the predicate of both premises : in the third, the subject of both : in the fourth, the predicate of the major premiss, and the subject of the minor.
Page 21 - The known quantities are represented by the first letters of the alphabet, a, b, c, d, &c. ; and the unknown, by the final letters, x, y, z, &c.
Page 45 - If a moving point possess simultaneously velocities which are represented in magnitude and direction by the two sides of a parallelogram drawn from a point, they are equivalent to a velocity which is represented in magnitude and direction by the diagonal of the parallelogram passing through the point.
Page 381 - Either this system of philosophy is merely relative or phenomenal, and cannot be known to be true, or else it is absolutely true, and can be known so to be. But it must be merely relative and phenomenal, if everything known by man is such. Its value, then, can be only relative and phenomenal, therefore it cannot be known to correspond with external reality, and cannot be asserted to be true ; and anybody who asserts that we can know it to be true, thereby asserts that it is false to say that our...
Page 29 - To divide one quantity by another, is to determine how often the latter is contained in the former, or what quantity multiplied by the latter will produce the former. Thus, to divide ab by a is to determine how often a must be taken to make up ab ; that is, what quantity multiplied by a will give ab ; which we know is b. From this consideration are derived all the rules for the division of algebraical quantities.
Page 290 - When the middle term is made the subject of the major premiss, and the predicate of the minor...