Introductory Modern Geometry of Point, Ray, and Circle |
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Page 2
... end . We may imagine a piece of Space cut out and colored ( to distinguish it from the rest of Space ) ; the piece will be bounded , but Space itself will remain unbounded . N. B. When we say that Space is unbounded , we do not mean ...
... end . We may imagine a piece of Space cut out and colored ( to distinguish it from the rest of Space ) ; the piece will be bounded , but Space itself will remain unbounded . N. B. When we say that Space is unbounded , we do not mean ...
Page 6
... ends of this part bound it off from the rest of the equator , but they them- selves form no part of the Equator . They are called points ; they have position merely , but no extent of any kind , neither length nor breadth nor thickness ...
... ends of this part bound it off from the rest of the equator , but they them- selves form no part of the Equator . They are called points ; they have position merely , but no extent of any kind , neither length nor breadth nor thickness ...
Page 11
... ends , and movable about one end fixed at a point ; then the other end will move always on a sphere - surface , which is the whole region where the moving end may be . Since Space is homœoidal around the fixed point , the surface ...
... ends , and movable about one end fixed at a point ; then the other end will move always on a sphere - surface , which is the whole region where the moving end may be . Since Space is homœoidal around the fixed point , the surface ...
Page 12
... end . Any surface may be dealt with as a plane by abstrac- 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 ...
... end . Any surface may be dealt with as a plane by abstrac- 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 ...
Page 14
... end for end . Such a line is called right , or straight , or direct , or a ray . Extended indefinitely , it cuts the whole plane into two halves pre- cisely alike along the ray itself . * N.B . The common line where the two spherical ...
... end for end . Such a line is called right , or straight , or direct , or a ray . Extended indefinitely , it cuts the whole plane into two halves pre- cisely alike along the ray itself . * N.B . The common line where the two spherical ...
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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.