Introductory Modern Geometry of Point, Ray, and Circle |
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Page 55
... parallel , through the point , to the straight line . 71. It cannot be too firmly insisted , nor too distinctly understood , that the existence of any non - intersector at all , and the existence of only one for any given point and ...
... parallel , through the point , to the straight line . 71. It cannot be too firmly insisted , nor too distinctly understood , that the existence of any non - intersector at all , and the existence of only one for any given point and ...
Page 56
... parallel to the base AB . Then a a ' , B = B ' ( why ? ) ; also a ' + y + B ' = S ; hence a + y + B = S ; i.e. ( Fig . 45 ) Theorem XXXI . - The sum of the ... Parallel Intercepts between parallels are equal 56 [ TH . XXXI . GEOMETRY .
... parallel to the base AB . Then a a ' , B = B ' ( why ? ) ; also a ' + y + B ' = S ; hence a + y + B = S ; i.e. ( Fig . 45 ) Theorem XXXI . - The sum of the ... Parallel Intercepts between parallels are equal 56 [ TH . XXXI . GEOMETRY .
Page 57
William Benjamin Smith. Theorem XXXII . - Parallel Intercepts between parallels are equal . Data : Land L ' , M and M , two pairs of parallels ( Fig . 46 ) . A / a M ட் a L B M ' FIG . 46 . Proof . Draw BD . Then the A ABD and CDB are ...
William Benjamin Smith. Theorem XXXII . - Parallel Intercepts between parallels are equal . Data : Land L ' , M and M , two pairs of parallels ( Fig . 46 ) . A / a M ட் a L B M ' FIG . 46 . Proof . Draw BD . Then the A ABD and CDB are ...
Page 58
... parallel ; similarly , AB and CD are parallel ; hence ABCD is a par- allelogram . Q. E. D. B ' . A 4 - side with opposite angles 58 [ TH . XXXIV . GEOMETRY .
... parallel ; similarly , AB and CD are parallel ; hence ABCD is a par- allelogram . Q. E. D. B ' . A 4 - side with opposite angles 58 [ TH . XXXIV . GEOMETRY .
Page 59
... parallel is a parallelogram . For the other two sides are equal and parallel ( why ? ) ; hence , etc. Q. E. D. 76. The foregoing properties and criteria of the parallel- ogram illustrate excellently the nature of a definition . This ...
... parallel is a parallelogram . For the other two sides are equal and parallel ( why ? ) ; hence , etc. Q. E. D. 76. The foregoing properties and criteria of the parallel- ogram illustrate excellently the nature of a definition . This ...
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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.