Introductory Modern Geometry of Point, Ray, and Circle |
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Page 11
... ; it is called a plane - surface . * N.B . A precise definition of this surface is the following : Take two points A and B and suppose two equal spherical bubbles formed about A and B as centres . Let INTRODUCTION . 11.
... ; it is called a plane - surface . * N.B . A precise definition of this surface is the following : Take two points A and B and suppose two equal spherical bubbles formed about A and B as centres . Let INTRODUCTION . 11.
Page 12
... plane as its path through Space . Hence we may define the plane as the region ( or surface ) where a point may be that is equidistant from two fixed points . Instead of region it is common to say locus , i.e. place . Briefly , then , a ...
... plane as its path through Space . Hence we may define the plane as the region ( or surface ) where a point may be that is equidistant from two fixed points . Instead of region it is common to say locus , i.e. place . Briefly , then , a ...
Page 13
... plane equidistant from a fixed point . Since the plane is homo- oidal , so too is this circle ( see Art . 10 ) ; a piece , called an arc , cut out and slipped round will everywhere fit on the circle . But turn it over and slip it round ...
... plane equidistant from a fixed point . Since the plane is homo- oidal , so too is this circle ( see Art . 10 ) ; a piece , called an arc , cut out and slipped round will everywhere fit on the circle . But turn it over and slip it round ...
Page 14
... plane , and in fact traces out the plane by its expansion as the bubbles expand . To get accurately the notion of the ray or straight line , we need another point C , and a third expanding bubble always equal to those about A and B. The ...
... plane , and in fact traces out the plane by its expansion as the bubbles expand . To get accurately the notion of the ray or straight line , we need another point C , and a third expanding bubble always equal to those about A and B. The ...
Page 15
... planes . A circle is the locus ( or path ) of a point in a plane at a fixed distance from a fixed point . It is homœoidal , but not reversible . It is also the locus ( or path ) of a point in space at a fixed distance from two points ...
... planes . A circle is the locus ( or path ) of a point in a plane at a fixed distance from a fixed point . It is homœoidal , but not reversible . It is also the locus ( or path ) of a point in space at a fixed distance from two points ...
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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.