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 79.
Σελίδα 4
... determined only by testing all its consequences , so that the real test of the validity of the hypotheses of geometry is in the validity of the theorems . realm of mathematics by using the non - committal word 4 MODERN MATHEMATICS.
... determined only by testing all its consequences , so that the real test of the validity of the hypotheses of geometry is in the validity of the theorems . realm of mathematics by using the non - committal word 4 MODERN MATHEMATICS.
Σελίδα 19
... determined by n points A1 , A2 , An is called the broken line A1 A2 A3 . . . An . A1 and An are called its ends , and it is said to join A1 and An . A single interval is a special case of a broken line . 1 A region is a set of points ...
... determined by n points A1 , A2 , An is called the broken line A1 A2 A3 . . . An . A1 and An are called its ends , and it is said to join A1 and An . A single interval is a special case of a broken line . 1 A region is a set of points ...
Σελίδα 26
... determined by b1b2 . . . bk . By Theorem 22 it separates this region , R , into two regions R / R " of which one at least is convex if R ; is not convex and both of which are convex if R ; is convex . Hence the k + 1 rays decompose the ...
... determined by b1b2 . . . bk . By Theorem 22 it separates this region , R , into two regions R / R " of which one at least is convex if R ; is not convex and both of which are convex if R ; is convex . Hence the k + 1 rays decompose the ...
Σελίδα 36
... determined as follows : Let O be the mid - point of the segment BC and O ′ the mid- point of the segment B'C " . If ... determine whether or not they are congruent . As an obvious corollary of the proof of this theorem we have ...
... determined as follows : Let O be the mid - point of the segment BC and O ′ the mid- point of the segment B'C " . If ... determine whether or not they are congruent . As an obvious corollary of the proof of this theorem we have ...
Σελίδα 57
... determine a plane . So also two planes intersect in a straight line and three planes in general have one point in ... determine a plane . a2 . Three planes determine a point . b1 . Two lines which have a common point determine a plane ...
... determine a plane . So also two planes intersect in a straight line and three planes in general have one point in ... determine a plane . a2 . Three planes determine a point . b1 . Two lines which have a common point determine a plane ...
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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...