Introductory Modern Geometry of Point, Ray, and Circle |
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Page 31
... ( Fig . 23 ) . Def . Rays that make right angles with one another are called normal ( or perpendicular ) to each other . N.B. The normal relation is mutual . How ? Def . Two angles whose sum is a right angle TH . IX . ] 31 CONGRUENCE .
... ( Fig . 23 ) . Def . Rays that make right angles with one another are called normal ( or perpendicular ) to each other . N.B. The normal relation is mutual . How ? Def . Two angles whose sum is a right angle TH . IX . ] 31 CONGRUENCE .
Page 48
... relation just established holds ; namely , the greater angle lies opposite a greater side . Q. E. D. 63. Theorem XXVII . — Every point on a mid - ray of an angle is equidistant from its sides . Data : the angle , MM ' the mid - ray , P ...
... relation just established holds ; namely , the greater angle lies opposite a greater side . Q. E. D. 63. Theorem XXVII . — Every point on a mid - ray of an angle is equidistant from its sides . Data : the angle , MM ' the mid - ray , P ...
Page 55
... relation of Axioms A and B : the one is the converse of the other . Observe also that the necessity of assuming the first lies in our igno- rance of the indefinitely great , and the occasion of assuming the other lies in our ignorance ...
... relation of Axioms A and B : the one is the converse of the other . Observe also that the necessity of assuming the first lies in our igno- rance of the indefinitely great , and the occasion of assuming the other lies in our ignorance ...
Page 56
... relation in which rays can stand to each other , and we must now use the new relation in the generation of new concepts . Theorem XXXII . - Parallel Intercepts between parallels are equal 56 [ TH . XXXI . GEOMETRY .
... relation in which rays can stand to each other , and we must now use the new relation in the generation of new concepts . Theorem XXXII . - Parallel Intercepts between parallels are equal 56 [ TH . XXXI . GEOMETRY .
Page 70
... relations in- volved , let him note carefully what concepts are present in the proposition , let him draw auxiliary lines and introduce auxiliary concepts at pleasure . But let him exhaust simple means before trying more complicated ...
... relations in- volved , let him note carefully what concepts are present in the proposition , let him draw auxiliary lines and introduce auxiliary concepts at pleasure . But let him exhaust simple means before trying more complicated ...
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Common terms and phrases
adjacent angles altitudes angle AOB angles equal anti-parallelogram axal symmetry Axiom axis of symmetry bisect called central angle central symmetry centre of symmetry chord circle K circles touch circumcircle concur congruent construction conversely Corollary corresponding angles curve Data diagonals diameter dimensions distance draw a circle Draw a ray drawn Elementary Algebra ends equal angles falls figure film fixed point Geometry given angle given point given ray half-rays halves homœoidal included angle inner angles inner mid-rays innerly intercept intersection isosceles join kite Let the student locus medial meet mid-points normal opposite angles opposite sides outer angle pairs parallel parallelogram plane point equidistant point of touch polygon position Problem Proof proposition radii radius reciprocal regular n-side reversible rhombus right angle round angle secant Solution Space sphere-surface straight angle subtended surface symmetric tangent tangent-lengths Theorem unequal vertex vertices
Popular passages
Page 95 - A circle is a closed plane curve, all points of which are equidistant from a point within called the center.
Page 35 - Two parallelograms, having two sides and the included angle of the one equal respectively to two sides and the included angle of the other, are equal.
Page 43 - BDN, have the three sides of the one equal respectively to the three sides of the other...
Page 70 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.