Monographs on Topics of Modern Mathematics: Relevant to the Elementary FieldJacob William Albert Young Longmans, Green, and Company, 1911 - 416 Seiten |
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Häufige Begriffe und Wortgruppen
a₁ algebraic equation angle of parallelism anharmonic ratio anti-derivative Assumption called coefficients complex quantities congruent conic continued fractions Corollary curve defined definite integral denoted derivative distance domain of rationality elementary elements equal Euclid Euclidean Euclidean geometry example expressed finite number follows formula fractions geometry given graph Hence imaginary integers intersect interval irrational line joining linear Lobachevskian mathematical method modulus multiple Non-Euclidean Geometry nth roots parallel perpendicular plane polar polynomial positive integer primitive root proof properties propositions proved quadratic equation rate of change rational functions rational numbers real numbers real points respectively Riemannian Riemannian geometry right angles roots of unity satisfy segment sheaf of rays sheaves sides solution square straight line symbol tangent Theorem theory theory of equations tion triangle u₁ uniquely determined unknowns values variable vertices x+4x zero
Beliebte Passagen
Seite 93 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Seite 83 - The points of intersection of the three pairs of opposite sides of a hexagon inscribed in a conic lie on one straight line.
Seite 259 - A sufficient condition for the maximum number of imaginary roots of an equation of the nth degree,
Seite 184 - Among the real points the points 1, 2, 3, ... [sec. 25. (15)] are called the positive integral points, and the points —1, —2, —3, . . . the negative integral points; all these, together with the point 0, form the subclass of " all integral points." All real points which can be expressed in the form ±m/n, where m and n are any positive integral points [sec. 25, (17)] together with the point 0, are called the rational points. The rational points which are not integral are called fractional;...
Seite 49 - X, in the order {AXB}; all points of the segment AB are said to be between A and B; the segment together with A and B is called the interval AB; the line AB consists of A and B and all points, X, in one of the orders { ABX}, {AXB,} {XAB}; and the ray AB consists of B and all points, X in one of the orders {AXB} and {ABX}; A is called the origin of the ray AB. III. If points C and D (Cy£) are on the line AB, then A is on the line CD.
Seite 85 - ... sides intersect in one point. 52. Pascal's theorem yields itself at once to the construction of a conic of which there are given five points, or four points and the tangent at one of them, or three points and the tangents at two of them. In the case of five points being given, if these are A, B, C, D, E, and they are joined in order, while an arbitrary line through A is drawn for sixth side of the inscribed hexagon, the hexagon is determined excepting only the fifth side and the sixth vertex....
Seite 259 - Annals of Mathematics, Vol. IV, 1903, p. 191. (5) Baker, "A balance for the solution of algebraic equations," American Mathematical Monthly, Vol. II, 1904, p. 224. (6) Emch, "Hydraulic solution of an algebraic equation of the nth degree," ibid., Vol. VIII, 1901, p. 58. (7) Moritz, " On certain proofs of the fundamental theorem of algebra," ibid., Vol. X, 1903, p. 159. (8) McClintock, "A method for calculating simultaneously all the roots of an equation," American Journal of Mathematics, Vol. XVII,...
Seite 198 - ... A + B is the vector sum of the vectors OA and OB. In case A and B are not in line with O, the point A + B is the fourth vertex of a parallelogram of which OA and OB are the sides (Fig. 3). Conversely, if any two points A and B are given, there is a definite point X such that A = B + X ; this point X is called the remainder, A minus B, and is denoted by A — B.
Seite 165 - A' is uniquely determined by A .] (h) For every element A and every positive integer n, there is an element Y such that Y [n] = A, where Y [ri] means YoYo • - *.oY to n elements.
Seite 175 - ... Repeated Addition. Multiples and Submultiples. The point A + A + A + . . . + A to n terms is called the nth multiple of A and is denoted by nA. The points U, 2U, 3U, . . . are denoted, for brevity, by 1, 2, 3, . . .. Conversely, if any point A, and any positive integer n are given, there is a definite point X such that nX = A ; this point X is called the nth submultiple of A, and is denoted by A/n. The points U/2, U/3, . . . are denoted, for brevity, by И, H Multiplication and Division. The...