Introductory Modern Geometry of Point, Ray, and Circle |
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Page 3
... length , its breadth , and its thickness . These are called its dimensions ; knowing them , we know the size completely . But to tell the size of a ball it is enough to tell one thing about it , namely , its diameter ; while to tell the ...
... length , its breadth , and its thickness . These are called its dimensions ; knowing them , we know the size completely . But to tell the size of a ball it is enough to tell one thing about it , namely , its diameter ; while to tell the ...
Page 6
... length . A line , then , has length , but neither breadth nor thickness . 5. Lastly , consider a part of a line , as of the Equator , say between longitudes 40 ° and 50 ° . The ends of this part bound it off from the rest of the equator ...
... length . A line , then , has length , but neither breadth nor thickness . 5. Lastly , consider a part of a line , as of the Equator , say between longitudes 40 ° and 50 ° . The ends of this part bound it off from the rest of the equator ...
Page 7
... length , its timbre , how high it is , how loud it is , how long it is , how rich it is . While , then , extents of higher dimensions may be unimaginable , they are not at all unreasonable . This doctrine of dimensions is of prime ...
... length , its timbre , how high it is , how loud it is , how long it is , how rich it is . While , then , extents of higher dimensions may be unimaginable , they are not at all unreasonable . This doctrine of dimensions is of prime ...
Page 8
... length , and it becomes for our reason a line . Lastly , we make a dot with pen or chalk or pencil ; it is a body , tri - dimensional , occupying Space . But we may dis- regard all its dimensions , and attend solely to the fact that it ...
... length , and it becomes for our reason a line . Lastly , we make a dot with pen or chalk or pencil ; it is a body , tri - dimensional , occupying Space . But we may dis- regard all its dimensions , and attend solely to the fact that it ...
Page 12
... - tion , being thought as homœoidal and reversible . 12. On this board , regarded as a plane , we draw a chalk- mark , abstract from all its dimensions but its length , and treat it as a line . This line is plainly 12 GEOMETRY .
... - tion , being thought as homœoidal and reversible . 12. On this board , regarded as a plane , we draw a chalk- mark , abstract from all its dimensions but its length , and treat it as a line . This line is plainly 12 GEOMETRY .
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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.