Introductory Modern Geometry of Point, Ray, and Circle |
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Page 54
... mid - point of OO ' ; on it as a pivot turn the whole right side of the plane round through a straight angle until O falls on O ' , and O ' falls on O. Then , since the angles about O and O ' are equal as above stated , the half - ray ...
... mid - point of OO ' ; on it as a pivot turn the whole right side of the plane round through a straight angle until O falls on O ' , and O ' falls on O. Then , since the angles about O and O ' are equal as above stated , the half - ray ...
Page 65
... mid - points of the trans- verse sides is the mid - parallel . M B L F N A D D ' FIG . 56 . Theorem XLII . - The mid - parallel of a trapezoid equals the half - sum of its bases . Let the student elicit the proof from the foregoing ...
... mid - points of the trans- verse sides is the mid - parallel . M B L F N A D D ' FIG . 56 . Theorem XLII . - The mid - parallel of a trapezoid equals the half - sum of its bases . Let the student elicit the proof from the foregoing ...
Page 69
William Benjamin Smith. 89. Theorem XLVII . The outer mid - rays of two angles and the inner mid - ray of the other angle of a △ concur . Let the student conduct the proof ( Fig . 60 ) . E2 FIG . 60 . Def . The points of concurrence are ...
William Benjamin Smith. 89. Theorem XLVII . The outer mid - rays of two angles and the inner mid - ray of the other angle of a △ concur . Let the student conduct the proof ( Fig . 60 ) . E2 FIG . 60 . Def . The points of concurrence are ...
Page 71
... points , M their mid - point . Show and state in words that 2 OM = OA + OB . 10. A , B , C are three points on a ray , A ' , B ' , C ' are mid - points of the tracts BC , CA , AB , and O is any point on the ray ; show that OA + OB + OC ...
... points , M their mid - point . Show and state in words that 2 OM = OA + OB . 10. A , B , C are three points on a ray , A ' , B ' , C ' are mid - points of the tracts BC , CA , AB , and O is any point on the ray ; show that OA + OB + OC ...
Page 72
William Benjamin Smith. point falls on the first the polygon is closed ; otherwise it is open . Unless otherwise stated , the polygon is supposed to be closed . The points ... mid - rays . 18. If two △ have their sides parallel or ...
William Benjamin Smith. point falls on the first the polygon is closed ; otherwise it is open . Unless otherwise stated , the polygon is supposed to be closed . The points ... mid - rays . 18. If two △ have their sides parallel or ...
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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.