The Project Gutenberg eBook #36640: Lectures on Elementary Mathematics

Parabolic curves, 130 et seq. Peletier, 52

Peyrard, 50

Physics, astronomy, and mechanics, curves of errors in, 123

Planetarium, 8

Point in space, position of a, 125

Polygon, problem of the circle and inscribed, 124

Polytechnic School, vi, xiii Positive roots, superior and

inferior limits of the, 98 Powers, 8 et seq.

Practice, theory and, 36 Present value, 12 Printing, invention of, 50

Probabilities, calculus of, 37 et seq.

Problems, 100

employment of curves in the solution of, 115–135

for solution, 53

Proclus, 50

Progressions, theory of, 10, 11 Proportion, 9 et seq.

Ptolemy, 50
Radical expressions in equations, 122

Radicals, cubic, 66

Ratios, constant, 1 et seq., 9 et seq., 35

Reality of roots, 67, 74, 75, 84

Regula falsi, 123, 134 Remainders

negative, 30 et seq. theory of, 28 et seq., 32

Romans, mathematics of the, 46 Roots

the arithmetical progression revealing the, 101 et seq., 108

of a biquadratic equation, 85 of equations of the third

degree, 61

limits of the positive and negative, 107

method for finding the limits

of, 99

multiple, 94

negative, 51

quantity less than the difference between any two, 101

the reality of the, 64, 67, 70,

74, 75, 84

separation of the, 101 smallest, 105 et seq.

superior and inferior limits of the positive, 98

Rule

Cardan’s, 58

of false, 123

of mixtures, 37 et seq.

of three, 9 et seq., 34 et seq.

Science

development of, viii et seq. history of, 18

Seven, tests of divisibility by, 29 Short-mind symbols, viii et seq. Signs + and , 48
−

Squaring of the circle, 53 Stenophrenic symbols,

viii et seq. Straight line, 130

Substitutions, 100 et seq., 111 Subtraction, new method of,

20 et seq.

Sum and difference, of two numbers, 47

Supposition, rule of, 125, 134 Symbols, viii et seq.

Tables, 124

expedient for supplying lacunæ in, 134

Tannery, M. Paul, 49 footnote, 136

Tartaglia, 51, 52 Temperament, theory of, 19 Theon, 50

Theory and practice, 36 Theory of remainders, utility of

the, 32

Third degree, equations of the, 61, 73

Three roots, reality of the, 84 Trial and error, rule of, 125, 134

Trisection of an angle, 52, 72

Turks, 49

Undetermined quantities, 73 Unity, three cubic roots of, 62 Unknown quantity, 46
Values

mean, 37 et seq. minimal, 119

Variations, calculus of, xi Vatican library, 49

Vieta, ix, 52, 55

Vlacq, 16
Wallis, ix

Wertheim, G., 49 footnote Woodhouse, xi

Xylander, 49