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addition algebra angle applied Assumption called circle coefficients common complex congruent consider construction contains continuous corresponding curve defined definition denoted derivative determined distance distinct divided division domain draw elementary elements equal equation evident example exists expressed fact factor figure follows formula four function fundamental geometry give given Hence important infinite integral intersect interval joining known least less mathematical means meet method multiple obtained operations opposite pairs parallel pass perpendicular plane positive possible postulates present prime primitive problem projective proof properties propositions proved quantities radicals range rational rays reduced region relation represent respectively root satisfy segment sides solution square statement straight line substitutions symbol Theorem theory triangle true unity unknowns zero
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 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...