Introductory Modern Geometry of Point, Ray, and Circle |
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Page 18
... equal circles . ANGLES . 21. The indefinite extent of a ray on one side of a point O , as OA , is called a half - ray : it has a beginning O , but no end . Two half - rays , OA and OA ' , which together make up a whole ray , are called ...
... equal circles . ANGLES . 21. The indefinite extent of a ray on one side of a point O , as OA , is called a half - ray : it has a beginning O , but no end . Two half - rays , OA and OA ' , which together make up a whole ray , are called ...
Page 19
... angles whose ends or arms may be made to fit on each other simultaneously are named equal ; they are also congruent . Two angles whose arms will not fit on each other simultaneously are unequal ; and that is the less angle whose end ...
... angles whose ends or arms may be made to fit on each other simultaneously are named equal ; they are also congruent . Two angles whose arms will not fit on each other simultaneously are unequal ; and that is the less angle whose end ...
Page 28
... AOA ; they are named straight ( or flat ) angles . = 37. Now , Halves of equals are equal ; - All straight angles are halves of equals ( namely , equal round angles ) ; Hence Theorem V. -All straight angles are equal . This 28 [ TH . IV .
... AOA ; they are named straight ( or flat ) angles . = 37. Now , Halves of equals are equal ; - All straight angles are halves of equals ( namely , equal round angles ) ; Hence Theorem V. -All straight angles are equal . This 28 [ TH . IV .
Page 29
William Benjamin Smith. Hence Theorem V. -All straight angles are equal . This argument here given in extenso is a specimen of a syllogism ( σvoyoμos = computation = thinking together ) . The first two propositions are called premisses ...
William Benjamin Smith. Hence Theorem V. -All straight angles are equal . This argument here given in extenso is a specimen of a syllogism ( σvoyoμos = computation = thinking together ) . The first two propositions are called premisses ...
Page 30
... angles are congruent , we may fit these two on each other ; i.e. we may fit OA and OA ' on PB and PB ' ; but BB ' is ... equal straight angles , and together they ( Fig . 22 ) form four angles a , ẞ , a ' , B ' . Two angles , as « and ẞ ...
... angles are congruent , we may fit these two on each other ; i.e. we may fit OA and OA ' on PB and PB ' ; but BB ' is ... equal straight angles , and together they ( Fig . 22 ) form four angles a , ẞ , a ' , B ' . Two angles , as « and ẞ ...
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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.