Introductory Modern Geometry of Point, Ray, and Circle |
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Page 12
... common to say locus , i.e. place . Briefly , then , a plane is the locus of a point equidis- tant from two fixed points . It is evident that the plane , as thus defined , is reversible ; for since the bubbles about A and B are all the ...
... common to say locus , i.e. place . Briefly , then , a plane is the locus of a point equidis- tant from two fixed points . It is evident that the plane , as thus defined , is reversible ; for since the bubbles about A and B are all the ...
Page 14
... common line where the two spherical bub- bles of Art . 10 meet is a circle , for it is plainly precisely alike all around ; it is homœoidal , being the intersection of two homœoidal surfaces , namely , the two equal sphere- surfaces ...
... common line where the two spherical bub- bles of Art . 10 meet is a circle , for it is plainly precisely alike all around ; it is homœoidal , being the intersection of two homœoidal surfaces , namely , the two equal sphere- surfaces ...
Page 21
... common notions . ) Some have no special reference to Geometry , but pervade all of our thinking about magnitudes ; such are ( 1 ) Things equal to the same thing are equal to each other . ( 2 ) If equals be added to , subtracted from ...
... common notions . ) Some have no special reference to Geometry , but pervade all of our thinking about magnitudes ; such are ( 1 ) Things equal to the same thing are equal to each other . ( 2 ) If equals be added to , subtracted from ...
Page 22
... common ; or , Only one ray can go through two fixed points ; or , A ray is fixed by two points . 26. A statement or declaration in words is called a prop- osition . The propositions with which we have to deal state geometric facts and ...
... common ; or , Only one ray can go through two fixed points ; or , A ray is fixed by two points . 26. A statement or declaration in words is called a prop- osition . The propositions with which we have to deal state geometric facts and ...
Page 30
... they ( Fig . 22 ) form four angles a , ẞ , a ' , B ' . Two angles , as « and ẞ , that have a common arm , are called adjacent . Accordingly we see at once : Theorem VIII . -Where two rays intersect , the sum 30 [ TH . VII . GEOMETRY .
... they ( Fig . 22 ) form four angles a , ẞ , a ' , B ' . Two angles , as « and ẞ , that have a common arm , are called adjacent . Accordingly we see at once : Theorem VIII . -Where two rays intersect , the sum 30 [ TH . VII . 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.