Introductory Modern Geometry of Point, Ray, and Circle |
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Page 17
... greater than CD , AB > CD . In either case , the tract BD or DB , between the two ends of the tracts , whose beginnings coin- cide , is called the difference of the two tracts , and we are said to subtract the one from the other ...
... greater than CD , AB > CD . In either case , the tract BD or DB , between the two ends of the tracts , whose beginnings coin- cide , is called the difference of the two tracts , and we are said to subtract the one from the other ...
Page 18
... 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 .
... 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 .
Page 19
... . Two angles whose arms will not fit on each other simultaneously are unequal ; and that is the less angle whose end - arm falls within the other angle when their beginnings coincide ; the other is the greater ; thus , INTRODUCTION . 19.
... . Two angles whose arms will not fit on each other simultaneously are unequal ; and that is the less angle whose end - arm falls within the other angle when their beginnings coincide ; the other is the greater ; thus , INTRODUCTION . 19.
Page 20
William Benjamin Smith. coincide ; the other is the greater ; thus , AOB > AOC ( Fig . 11 ) . 24. We sum angles precisely as we sum tracts ; we lay off a , B , etc. , around O , making the end of each the begin- ning of the next : the ...
William Benjamin Smith. coincide ; the other is the greater ; thus , AOB > AOC ( Fig . 11 ) . 24. We sum angles precisely as we sum tracts ; we lay off a , B , etc. , around O , making the end of each the begin- ning of the next : the ...
Page 22
... greater than any of its parts . ( 5 ) If a necessary consequence of any supposition is false , the supposition itself is false . Others concern Geometry especially , as : ( 6 ) All planes are congruent . ( 7 ) Two rays can meet in only ...
... greater than any of its parts . ( 5 ) If a necessary consequence of any supposition is false , the supposition itself is false . Others concern Geometry especially , as : ( 6 ) All planes are congruent . ( 7 ) Two rays can meet in only ...
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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.