Introductory Modern Geometry of Point, Ray, and Circle |
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Page 81
... reciprocal , and the two pairs of reciprocals together make up another more complex pair of reciprocals . In this latter pair we find our definition fully exemplified . To O and O ' correspond Z and L ' ; to the rays through O and O ...
... reciprocal , and the two pairs of reciprocals together make up another more complex pair of reciprocals . In this latter pair we find our definition fully exemplified . To O and O ' correspond Z and L ' ; to the rays through O and O ...
Page 82
... reciprocals must correspond also three rays fixing a triangle in the other reciprocal ; hence , in general , triangle corre- sponds to triangle in reciprocals . But notice : the sides of one correspond to the vertices of the other ...
... reciprocals must correspond also three rays fixing a triangle in the other reciprocal ; hence , in general , triangle corre- sponds to triangle in reciprocals . But notice : the sides of one correspond to the vertices of the other ...
Page 86
... reciprocals . The reciprocals of the two points A and A ' symmetric as to the axis X will be two rays L , L ' , symmetric as to the centre S. But rays symmetric as to a centre are parallel ( why ? ) ; hence we have two parallels ...
... reciprocals . The reciprocals of the two points A and A ' symmetric as to the axis X will be two rays L , L ' , symmetric as to the centre S. But rays symmetric as to a centre are parallel ( why ? ) ; hence we have two parallels ...
Page 87
... reciprocal of a △ in axal symmetry is a △ ( 3 - angle or 3 - point ) in central sym- metry , we should have said , accurately , that the recipro- cal of a △ in axal symmetry is a 3 - side ( or trilateral ) in central symmetry , which ...
... reciprocal of a △ in axal symmetry is a △ ( 3 - angle or 3 - point ) in central sym- metry , we should have said , accurately , that the recipro- cal of a △ in axal symmetry is a 3 - side ( or trilateral ) in central symmetry , which ...
Page 89
... reciprocal of both kite and anti- parallelogram , which are thus seen to be really one . 107. Central symmetry does not in general imply any- thing at all with respect to axal symmetry in a figure . We may draw through any point S any ...
... reciprocal of both kite and anti- parallelogram , which are thus seen to be really one . 107. Central symmetry does not in general imply any- thing at all with respect to axal symmetry in a figure . We may draw through any point S any ...
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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.