Introductory Modern Geometry of Point, Ray, and Circle |
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Page 96
... radius are congruent , and all quadrants of the same radius are congruent . Corollary 3. Any circle may be slipped round at will upon itself about its centre as a pivot , like a wheel about its axle , without changing in the least the ...
... radius are congruent , and all quadrants of the same radius are congruent . Corollary 3. Any circle may be slipped round at will upon itself about its centre as a pivot , like a wheel about its axle , without changing in the least the ...
Page 102
... radius ) at its end . Such a normal to a radius at its end is called a tangent to the circle at the point of tangence ( or touch or contact ) C. Def . A ray normal to a tangent to a curve at the point of touch is called normal to the ...
... radius ) at its end . Such a normal to a radius at its end is called a tangent to the circle at the point of tangence ( or touch or contact ) C. Def . A ray normal to a tangent to a curve at the point of touch is called normal to the ...
Page 112
... radius of the 9 - point circle is half the radius of the circumcircle . 135. Def . A Polygon all of whose sides touch a circle is said to be circumscribed about it , and the circle is said to be inscribed in the polygon . Theorem LXXIII ...
... radius of the 9 - point circle is half the radius of the circumcircle . 135. Def . A Polygon all of whose sides touch a circle is said to be circumscribed about it , and the circle is said to be inscribed in the polygon . Theorem LXXIII ...
Page 116
... radius , and draw the ʼn chords B K E FIG . 94 . subtending the n equal central angles . These chords are all equal ( why ? ) , and subtend equal arcs , and they form an n - side . Moreover , the angle between two consecutive sides is ...
... radius , and draw the ʼn chords B K E FIG . 94 . subtending the n equal central angles . These chords are all equal ( why ? ) , and subtend equal arcs , and they form an n - side . Moreover , the angle between two consecutive sides is ...
Page 117
... radius CB draw another circle . The fourth vertex D must lie on this circle ( why ? ) . If it lie on the circle K , then the angle BCD = angle ABC , as is the case in the regular n - side . Neither can it lie off of K , as at D ' or D ...
... radius CB draw another circle . The fourth vertex D must lie on this circle ( why ? ) . If it lie on the circle K , then the angle BCD = angle ABC , as is the case in the regular n - side . Neither can it lie off of K , as at D ' or D ...
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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.