Monographs on Topics of Modern Mathematics, Relevant to the Elementary FieldJacob William Albert Young Longmans, Green and Company, 1911 - 416 σελίδες |
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Αποτελέσματα 1 - 5 από τα 58.
Σελίδα
... Circles- Parallel Lines - Mensuration - Three - Dimensional Space - Con- clusion . II . MODERN PURE GEOMETRY * . Introduction - Simple Elements in Geometry - The Principle of Duality - Principle of Continuity - Points at Infinity ...
... Circles- Parallel Lines - Mensuration - Three - Dimensional Space - Con- clusion . II . MODERN PURE GEOMETRY * . Introduction - Simple Elements in Geometry - The Principle of Duality - Principle of Continuity - Points at Infinity ...
Σελίδα
... Circle - Connection between Regular Polygons and Roots of Unity - De Moivre's Theorem - Regular Pentagon and Deca- ' gon - Regular Polygon of 17 Sides - Construction of the Regular Polygon of 17 Sides - Gauss's Theory of Regular ...
... Circle - Connection between Regular Polygons and Roots of Unity - De Moivre's Theorem - Regular Pentagon and Deca- ' gon - Regular Polygon of 17 Sides - Construction of the Regular Polygon of 17 Sides - Gauss's Theory of Regular ...
Σελίδα 2
... VII . CONGRUENCE OF ANGLES . VIII . INTERSECTIONS OF CIRCLES . 3 5 9 14 19 27 30 32 IX . PARALLEL LINES . 43 X. MENSURATION . XI . THREE - DIMENSIONAL SPACE .. XII . CONCLUSION . 44 47 49 I THE FOUNDATIONS OF GEOMETRY * I. By OSWALD VEBLEN.
... VII . CONGRUENCE OF ANGLES . VIII . INTERSECTIONS OF CIRCLES . 3 5 9 14 19 27 30 32 IX . PARALLEL LINES . 43 X. MENSURATION . XI . THREE - DIMENSIONAL SPACE .. XII . CONCLUSION . 44 47 49 I THE FOUNDATIONS OF GEOMETRY * I. By OSWALD VEBLEN.
Σελίδα 32
... circle . O is called its centre and any one of the inter- vals OX is called a radius . The two radii on any line . through O constitute a ... circle . Another assumption , however , is necessary 32 MODERN MATHEMATICS INTERSECTIONS OF CIRCLES.
... circle . O is called its centre and any one of the inter- vals OX is called a radius . The two radii on any line . through O constitute a ... circle . Another assumption , however , is necessary 32 MODERN MATHEMATICS INTERSECTIONS OF CIRCLES.
Σελίδα 33
... circle in the same plane has in common with the other circle at least one point on each side of the line AB . Definition . A triangle is said to be isosceles if two of its sides are congruent and to be equilateral if all three are ...
... circle in the same plane has in common with the other circle at least one point on each side of the line AB . Definition . A triangle is said to be isosceles if two of its sides are congruent and to be equilateral if all three are ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
algebraic equation angle of parallelism anharmonic ratio anti-derivative Assumption called coefficients complete quadrangle complex quantities congruent conic convex regions Corollary curve defined definition degree denoted distance domain of rationality elementary elements equal Euclid Euclidean Euclidean geometry example expressed fact factor finite number follows formula fundamental circle given gruent harmonic Hence imaginary imaginary units infinitely distant integers integral function interval irrational lines joining Lobachevskian mathematical method multiple non-Euclidean geometries nth roots pairs of corresponding parallel perpendicular polar polynomial positive integer prime proof properties propositions proved quadratic equation quadrilateral rational functions rational numbers real numbers real points respectively Riemannian geometry right angles roots of unity satisfy sheaf of rays sheaves sides solution straight line substitutions symbol tangent Theorem theory of equations tion uniquely determined unknowns values vertices zero
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 83 - The points of intersection of the three pairs of opposite sides of a hexagon inscribed in a conic lie on one straight line.
Σελίδα 41 - If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles.
Σελίδα 259 - A sufficient condition for the maximum number of imaginary roots of an equation of the nth degree,
Σελίδα 354 - A proposed construction is possible by ruler and compasses if, and only if, the numbers which define analytically the desired geometric elements can be derived from those defining the given elements by a finite number of rational operations and extractions of real square roots.
Σελίδα 32 - SSS); two sides and the included angle of one triangle are congruent to the corresponding parts...
Σελίδα 391 - The third period extends from the middle of the eighteenth century to the present time...
Σελίδα 362 - Let a real number which can be obtained from the integers by a finite number of rational operations and extractions of square roots be called a quadratic number. A, B, C are any three points not in a straight line such that AC and BC are quadratic in terms of AB.
Σελίδα 195 - This system satisfies all the postulates except Postulate 27. It is larger than the system of ordinary complex quantities, and contains that system just as the system of ordinary complex quantities contains the system of real quantities. Postulate 27 is therefore a restrictive condition. 36. What is algebra? We are now in a position to answer the question, " What is the algebra of complex quantities?
Σελίδα 184 - 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; the fractional points lie between the integral points. All real points which are not rational are called irrational. That not all the real points are "rational...