## Elements of Geometry |

### From inside the book

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Page 22

... BC ; therefore the figure ABCD is a parallelogram , THEOREM . 85. The two diagonals AC , DB ( fig . 45 ) , of a parallelogram mutually

... BC ; therefore the figure ABCD is a parallelogram , THEOREM . 85. The two diagonals AC , DB ( fig . 45 ) , of a parallelogram mutually

**bisect**each other . Demonstration . If we compare the triangle ADO with the 22 Elements of Geometry . Page 25

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**bisects**the circle and its cir- Fig . 49 . cumference . Demonstration . If the figure AEB be 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 ... Page 27

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**bisects**this chord and the arc subtended by it AGB . Demonstration . Draw the radii CA , CB ; these radii are , with respect to the perpendicular CD , two equal oblique lines ; there- fore they are equally distant from the perpendicular ... Page 28

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**bisect**these two straight lines by the perpendiculars DE , FG ; these perpendiculars will meet in a point O. For the lines DE , FG , will necessarily cut each other , if they are not parallel . Let us suppose that they are parallel ... Page 29

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**Bisect**Fig . 53 these chords by the perpendiculars CF , CG , and draw the radii CA , CD . The right - angled triangles CAF , DCG , have the hypothe- nuses CA , CD , equal ; moreover , the side AF , the half of AB , is equal to the side ...### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC 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 angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence