Introductory Modern Geometry of Point, Ray, and Circle |
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Page 3
... we wish to tell exactly where a thing is in Space , to tell two things about it . Thus , at this moment the bright star Jupiter is shining exactly in the south ; we also know its altitude , how high it is above INTRODUCTION . 3.
... we wish to tell exactly where a thing is in Space , to tell two things about it . Thus , at this moment the bright star Jupiter is shining exactly in the south ; we also know its altitude , how high it is above INTRODUCTION . 3.
Page 4
William Benjamin Smith. also know its altitude , how high it is above the horizon ( this altitude is measured angularly — a term to be explained hereafter , but with which we have no present concern ) . But the knowledge of these two ...
William Benjamin Smith. also know its altitude , how high it is above the horizon ( this altitude is measured angularly — a term to be explained hereafter , but with which we have no present concern ) . But the knowledge of these two ...
Page 67
... altitude . Theorem XLV . - The altitudes of a △ concur . Proof . Using the preceding figure , draw the △ A'B'C ' . Its sides are parallel to the sides of ABC ( why ? ) ; hence its altitudes are the mid - normals L , M , N ; and these ...
... altitude . Theorem XLV . - The altitudes of a △ concur . Proof . Using the preceding figure , draw the △ A'B'C ' . Its sides are parallel to the sides of ABC ( why ? ) ; hence its altitudes are the mid - normals L , M , N ; and these ...
Page 68
William Benjamin Smith. Def . The point of concurrence of altitudes is called the orthocentre ( or alticentre ) of the A. Def . In a right △ the side opposite the right angle is called the hypotenuse ( = subtense under - stretch ) ...
William Benjamin Smith. Def . The point of concurrence of altitudes is called the orthocentre ( or alticentre ) of the A. Def . In a right △ the side opposite the right angle is called the hypotenuse ( = subtense under - stretch ) ...
Page 73
... altitudes , ( 2 ) when they are medials , ( 3 ) when they are mid - rays of angles A and B , ( 4 ) when MN is normal to the mid - normal of AB . 24. P is any point within the △ ABC ; show that AP + BP < AC + CB , AP + PB + CP > } ( AB ...
... altitudes , ( 2 ) when they are medials , ( 3 ) when they are mid - rays of angles A and B , ( 4 ) when MN is normal to the mid - normal of AB . 24. P is any point within the △ ABC ; show that AP + BP < AC + CB , AP + PB + CP > } ( AB ...
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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.