Elements of Geometry |
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Page 3
... , or solids , are equal , when , being applied the one to the other , they coin- cide with each other entirely , that is , when they exactly fill the same space . Fig . 42 . PART FIRST . OF PLANE FIGURES . SECTION FIRST . Axioms . 3.
... , or solids , are equal , when , being applied the one to the other , they coin- cide with each other entirely , that is , when they exactly fill the same space . Fig . 42 . PART FIRST . OF PLANE FIGURES . SECTION FIRST . Axioms . 3.
Page 4
... applied to AB , so that the point E will fall upon A , and the point F upon B. These two lines , thus placed , will co- incide with each other throughout ; otherwise there would be two straight lines between A and B , which is ...
... applied to AB , so that the point E will fall upon A , and the point F upon B. These two lines , thus placed , will co- incide with each other throughout ; otherwise there would be two straight lines between A and B , which is ...
Page 23
... applied to AFB , so that the base AB may be common to both , the curved line AEB must fall exactly upon the curved line AFB ; otherwise , there would be points in the one or the other unequally distant from the centre , which is ...
... applied to AFB , so that the base AB may be common to both , the curved line AEB must fall exactly upon the curved line AFB ; otherwise , there would be points in the one or the other unequally distant from the centre , which is ...
Page 24
... applied exactly to the semicircle ENGF , and then the curved line AMDB will coincide entirely with the curved line ENGF ; but the portion AMD being sup- posed equal to the portion ENG , the point D will fall upon G ; therefore the chord ...
... applied exactly to the semicircle ENGF , and then the curved line AMDB will coincide entirely with the curved line ENGF ; but the portion AMD being sup- posed equal to the portion ENG , the point D will fall upon G ; therefore the chord ...
Page 42
... applied to an arc of the same radius , as a straight line is applied to a straight line . We shall thus obtain a common measure of the arcs CD , EF , if they have one , and their ratio in numbers . This ratio will be the same as that of ...
... applied to an arc of the same radius , as a straight line is applied to a straight line . We shall thus obtain a common measure of the arcs CD , EF , if they have one , and their ratio in numbers . This ratio will be the same as that of ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence