Elements of Geometry |
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Page vi
... parallel lines , & c . The second section , entitled the circle , treats of the most sim- ple properties of the circle , and those of chords , of tangents , and of the measure of angles by the arcs of a circle . These two sections are ...
... parallel lines , & c . The second section , entitled the circle , treats of the most sim- ple properties of the circle , and those of chords , of tangents , and of the measure of angles by the arcs of a circle . These two sections are ...
Page 2
... parallel ( fig . 5 ) , when , being situated in the same plane and produced ever so far both ways , they do not meet . 13. A plane figure is a plane terminated on all sides by lines . If the lines are straight , the space which they ...
... parallel ( fig . 5 ) , when , being situated in the same plane and produced ever so far both ways , they do not meet . 13. A plane figure is a plane terminated on all sides by lines . If the lines are straight , the space which they ...
Page 4
... parallel Lines . THEOREM . 27. ALL right angles are equal . Demonstration . Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH to EF , the angles ACD , EGH , will be equal . Take the four distances CA , CB ...
... parallel Lines . THEOREM . 27. ALL right angles are equal . Demonstration . Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH to EF , the angles ACD , EGH , will be equal . Take the four distances CA , CB ...
Page 13
... parallel , that is , they will not meet , however far they are produced ( 12 ) . Demonstration . If they could meet in a point O on one side or the other of the line AB , there would be two perpendiculars drawn from the same point O to ...
... parallel , that is , they will not meet , however far they are produced ( 12 ) . Demonstration . If they could meet in a point O on one side or the other of the line AB , there would be two perpendiculars drawn from the same point O to ...
Page 14
... parallel . Demonstration . From the point G , the middle of AB , draw the straight line EGF perpendicular to AC ; this line will be perpen- dicular to BD . Indeed the sum GAE รท GBD is , by hypothesis , equal to two right angles , and ...
... parallel . Demonstration . From the point G , the middle of AB , draw the straight line EGF perpendicular to AC ; this line will be perpen- dicular to BD . Indeed the sum GAE รท GBD is , by hypothesis , equal to two right angles , and ...
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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