Introductory Modern Geometry of Point, Ray, and Circle |
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Page 1
William Benjamin Smith. GEOMETRY . INTRODUCTION . 1. Geometry is the Doctrine of Space . What is Space ? On opening our eyes we see objects around us in endless number and variety : the book here , the table there , the tree yonder ...
William Benjamin Smith. GEOMETRY . INTRODUCTION . 1. Geometry is the Doctrine of Space . What is Space ? On opening our eyes we see objects around us in endless number and variety : the book here , the table there , the tree yonder ...
Page 2
... Space is homœoidal ; i.e. it is precisely alike through- out its whole extent . Any body may just as well be here , there , or yonder , so far as Space is concerned . A mere change of place in nowise affects the Space in which the ...
... Space is homœoidal ; i.e. it is precisely alike through- out its whole extent . Any body may just as well be here , there , or yonder , so far as Space is concerned . A mere change of place in nowise affects the Space in which the ...
Page 3
... Space is continuous . There are no gaps nor holes in it , where it would be impossible for a body to be . A body may move about in Space anywhere and everywhere , ever so much or ever so little . Space is itself simply where a body may ...
... Space is continuous . There are no gaps nor holes in it , where it would be impossible for a body to be . A body may move about in Space anywhere and everywhere , ever so much or ever so little . Space is itself simply where a body may ...
Page 4
... the ceiling is not fourteen feet high , contra- dicting what is already said . In general , with respect to any position in Space it is necessary to know three independent All facts ( or data ) , and it is 4 GEOMETRY .
... the ceiling is not fourteen feet high , contra- dicting what is already said . In general , with respect to any position in Space it is necessary to know three independent All facts ( or data ) , and it is 4 GEOMETRY .
Page 5
... Space is known completely when , and only when , three independent data are known about it , we say that Space is triply or three- fold extended , or has three dimensions . The dimensions are any three independent things that it is ...
... Space is known completely when , and only when , three independent data are known about it , we say that Space is triply or three- fold extended , or has three dimensions . The dimensions are any three independent things that it is ...
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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.