Introductory Modern Geometry of Point, Ray, and Circle |
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Page 6
... fall together , and the film would be a surface ; namely , the outside of the Space within and the inside of the Space without . 4. Consider now once more this earth - surface , still viewed as a smooth level sheet of water . From ...
... fall together , and the film would be a surface ; namely , the outside of the Space within and the inside of the Space without . 4. Consider now once more this earth - surface , still viewed as a smooth level sheet of water . From ...
Page 15
... fall are equidistant from A , and no other points are equidistant with them . They all lie on a closed surface , called a sphere - surface . All points within this surface are said to be less distant , and all points without are said to ...
... fall are equidistant from A , and no other points are equidistant with them . They all lie on a closed surface , called a sphere - surface . All points within this surface are said to be less distant , and all points without are said to ...
Page 16
... fall upon each other in this superposition are said to correspond . It is manifest that all planes are congruent and all rays are congruent . Rays and planes are unbounded , but whether or not they are finite is a question that we are ...
... fall upon each other in this superposition are said to correspond . It is manifest that all planes are congruent and all rays are congruent . Rays and planes are unbounded , but whether or not they are finite is a question that we are ...
Page 17
... fall on the end D , the tracts are unequal , and we write AB + CD . If B falls between C and D , then AB is called less than CD , AB < CD ; but if D falls between A and B , then AB is called greater than CD , AB > CD . In either case ...
... fall on the end D , the tracts are unequal , and we write AB + CD . If B falls between C and D , then AB is called less than CD , AB < CD ; but if D falls between A and B , then AB is called greater than CD , AB > CD . In either case ...
Page 18
... is a mag- nitude : it may be greater or less . Suppose OA and OB to be two very fine needles pivoted at O ; then OB may fall exactly on OA , or it may be turned round from OA ; and I 1 the amount of turning from OA to OB , or 18 GEOMETRY .
... is a mag- nitude : it may be greater or less . Suppose OA and OB to be two very fine needles pivoted at O ; then OB may fall exactly on OA , or it may be turned round from OA ; and I 1 the amount of turning from OA to OB , or 18 GEOMETRY .
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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.