## Elements of Geometry |

### From inside the book

Results 1-5 of 25

Page 2

...

...

**parallelogram**( fig . 13 ) , which has its opposite sides par- allel ; The rhombus or lozenge ( fig . 14 ) , which has its sides equal without having its angles right angles ; The trapezoid ( fig . 15 ) , which has two only of its sides ... Page 20

...

...

**parallelogram**are equal , and the oppo- site angles also are equal . Demonstration . Draw the diagonal BD ( fig . 44 ) ; the two triangles ADB , DBC , have the side BD common ; moreover , on account of the parallels AD , BC , the angle ... Page 21

...

...

**parallelogram**. THEOREM . 87. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral Fig . 44 . are equal and parallel , the two other sides will also be equal and parallel , and the figure ABCD will be a**parallelogram**... Page 38

...

...

**parallelogram**required . For , by construction , the opposite sides are equal , therefore the figure is a**parallelogram**( 86 ) , and it is formed with the given adjacent sides and included angle . 148. Corollary . If the given angle be ... Page 43

...

...

**parallelograms**ABCD , ABEF ; since they are supposed to have the same altitude , the sides DC , FE , opposite to the bases , will be situated in a line parallel to AB ( 69 ) . Now , by the nature of a**parallelogram**, AD = BC ( 84 ) ...### Other editions - View all

### 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