Introductory Modern Geometry of Point, Ray, and Circle |
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Page 2
... bounded , but Space itself will remain unbounded . N. B. When we say that Space is unbounded , we do not mean that it is infinite . Suppose an earthquake to sink all the land beneath the level of the sea , and suppose this latter at ...
... bounded , but Space itself will remain unbounded . N. B. When we say that Space is unbounded , we do not mean that it is infinite . Suppose an earthquake to sink all the land beneath the level of the sea , and suppose this latter at ...
Page 7
... bounded by points , and themselves bound surfaces ; surfaces are bounded by lines , and themselves bound spaces ; spaces are bounded by surfaces , and themselves bound - what ? If anything at all , it must be some extent of still higher ...
... bounded by points , and themselves bound surfaces ; surfaces are bounded by lines , and themselves bound spaces ; spaces are bounded by surfaces , and themselves bound - what ? If anything at all , it must be some extent of still higher ...
Page 16
... bounded by two end - points , A and B , and is finite ; the one is named an arc ( Fig . 5 ) , the other a tract , sect , or line - segment . Each is denoted by the two letters denoting the ends , as the tract AB , the arc AB . Sometimes ...
... bounded by two end - points , A and B , and is finite ; the one is named an arc ( Fig . 5 ) , the other a tract , sect , or line - segment . Each is denoted by the two letters denoting the ends , as the tract AB , the arc AB . Sometimes ...
Page 30
... bounded by counter half - rays . Then we may prove Theorem V. thus : The ends of all straight angles are pairs of counter half- rays ( or form whole rays ) ; But all such pairs ( or whole rays ) are congruent ( by Theorem I ...
... bounded by counter half - rays . Then we may prove Theorem V. thus : The ends of all straight angles are pairs of counter half- rays ( or form whole rays ) ; But all such pairs ( or whole rays ) are congruent ( by Theorem I ...
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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.