Introductory Modern Geometry of Point, Ray, and Circle |
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Page 12
... sides of the plane , will make no dif- ference whatever . Thus the plane cuts the Space evenly half in two ; and since Space itself is homœoidal , so also is this section or surface that halves it exactly . The superiority of this ...
... sides of the plane , will make no dif- ference whatever . Thus the plane cuts the Space evenly half in two ; and since Space itself is homœoidal , so also is this section or surface that halves it exactly . The superiority of this ...
Page 18
... side of a point O , as OA , is called a half - ray : it has a beginning O , but no end . Two half - rays , OA and OA ' , which together make up a whole ray , are called opposite or counter ( Fig . 10 ) . Now let two half - rays , OA and ...
... side of a point O , as OA , is called a half - ray : it has a beginning O , but no end . Two half - rays , OA and OA ' , which together make up a whole ray , are called opposite or counter ( Fig . 10 ) . Now let two half - rays , OA and ...
Page 25
... Think of OA as held fast and of OB as turning about the pivot O , starting from the position OA . As it turns ( counter - clockwise ) , the ( Fig . 15 ) angle - side of OA back to the under side of TH . II . ] 25 CONGRUENCE .
... Think of OA as held fast and of OB as turning about the pivot O , starting from the position OA . As it turns ( counter - clockwise ) , the ( Fig . 15 ) angle - side of OA back to the under side of TH . II . ] 25 CONGRUENCE .
Page 26
William Benjamin Smith. - side of OA back to the under side of OA , or the full spread around the point O , is called a ... sides of OA are exactly the same in position , and are distinguished only in thought . ( Think of a circular piece ...
William Benjamin Smith. - side of OA back to the under side of OA , or the full spread around the point O , is called a ... sides of OA are exactly the same in position , and are distinguished only in thought . ( Think of a circular piece ...
Page 28
... side of OA , the angle AOB begins by being less than BOA and ends by ( Fig . 19 ) being greater than BOA . The plane Α B A FIG . 19 . is continuous , the turning is continuous , the change in size is continuous ; hence , in passing from ...
... side of OA , the angle AOB begins by being less than BOA and ends by ( Fig . 19 ) being greater than BOA . The plane Α B A FIG . 19 . is continuous , the turning is continuous , the change in size is continuous ; hence , in passing from ...
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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.