Introductory Modern Geometry of Point, Ray, and Circle |
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Page 26
... angle ( or round angle , or circum - angle , or perigon ) . Think of a fan opened until the first rib falls on the last . Note that the upper and under sides of OA are exactly the same in position , and are distinguished only in thought ...
... angle ( or round angle , or circum - angle , or perigon ) . Think of a fan opened until the first rib falls on the last . Note that the upper and under sides of OA are exactly the same in position , and are distinguished only in thought ...
Page 27
... round angle AOA into two angles , AOB and BOA . The end OB of the first falls on the beginning , OB , of the second ; while B B A Ж FIG . 17 . E A the end , OA , of the second falls on the beginning , OA , of the first . Hence the round ...
... round angle AOA into two angles , AOB and BOA . The end OB of the first falls on the beginning , OB , of the second ; while B B A Ж FIG . 17 . E A the end , OA , of the second falls on the beginning , OA , of the first . Hence the round ...
Page 28
... round from the upper to the under 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 ...
... round from the upper to the under 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 ...
Page 29
... round angle AOA ; hence each is half of AOA ; i.e. each is a straight angle . Q. E. D. 39. Theorem VII . - Conversely , The half - rays bounding a straight angle are counter . Α A B ' P FIG . 21 . Let OA and OA ' bound a straight angle ...
... round angle AOA ; hence each is half of AOA ; i.e. each is a straight angle . Q. E. D. 39. Theorem VII . - Conversely , The half - rays bounding a straight angle are counter . Α A B ' P FIG . 21 . Let OA and OA ' bound a straight angle ...
Page 30
... round angle about O into two equal straight angles , and together they ( Fig . 22 ) form four angles a , ẞ , a ' , B ' . Two angles , as « and ẞ , that have a common arm , are called adjacent . Accordingly we see at once : Theorem VIII ...
... round angle about O into two equal straight angles , and together they ( Fig . 22 ) form four angles a , ẞ , a ' , B ' . Two angles , as « and ẞ , that have a common arm , are called adjacent . Accordingly we see at once : Theorem VIII ...
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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.