Lectures on the Principles of Demonstrative Mathematics

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A. and C. Black, 1843 - Algebra - 147 pages

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Page 64 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Page 38 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 52 - Any two sides of a triangle are together greater than the third side.
Page 96 - ... of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth...
Page 122 - Whatever form is algebraically equivalent to another when expressed in general symbols, must continue to be equivalent whatever those symbols denote.
Page 17 - It is certain that from its completeness, uniformity and faultlessness, from its arrangement and progressive character, and from the universal adoption of the completest and best line of argument, Euclid's " Elements " stand preeminently at the head of all human productions.
Page 38 - Of four-sided figures, a square is that which has all its sides equal, and all its angles right angles.
Page 67 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.
Page 88 - But when four magnitudes are proportionals, if the first be greater than the third, the second is greater than the fourth ; and if equal, equal; if less, less; (v.
Page 25 - That all our cognition," he says, " begins with experience, there is not any doubt ; for how otherwise should the faculty of cognition be awakened into exercise, if this did not occur through objects which affect our senses...

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