## Elements of Geometry |

### From inside the book

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**parallelogram**( fig . 13 ) , which has its opposite sides par- allel ; Fig . 14 . The rhombus or lozenge ( fig . 14 ) , which has its sides equal , without having its angles right angles ; Fig . 15 . The trapezoid ( fig . 15 ) , which ... Page 21

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**parallelogram**are equal , and the opposite angles also are equal . Demonstration . Draw the diagonal BD ( fig . 44 ) ; the two Fig . 44 triangles ADB , DBC , have the side BD common ; moreover , on account of the parallels AD , BC , the ... Page 22

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**parallelogram**are equal . Again , from the equality of the same triangles , it follows , that the angle A = C , and also that the angle ADC , composed of the two angles ADB , BDC , is equal to the angle ABC , com- posed of the two ... Page 23

... , and are consequently equal ; whence it follows , that the angle AOB = BOC , and that thus the two diagonals of a rhom- bus cut each other mutually at right angles . Fig . 46 . Fig . 47 . SECTION SECOND Of

... , and are consequently equal ; whence it follows , that the angle AOB = BOC , and that thus the two diagonals of a rhom- bus cut each other mutually at right angles . Fig . 46 . Fig . 47 . SECTION SECOND Of

**Parallelograms**. 23. Page 40

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**parallelogram**being given together with the included angle C , to construct the**parallelogram**. Solution . Draw the line DE = A ; make the angle FDE = C , and take DF = B ; describe two arcs , one from the point F , as a centre , with ...### 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 convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent 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 pyramid S-ABC 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