## Elements of Geometry |

### From inside the book

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**quadrilateral**; that of five sides , a pentagon ; that of six , a hexa- gon , & c . 15. A triangle is denominated equilateral ( fig . 7 ) , when the Fig , 8. three sides are equal , isosceles ( fig . 8 ) , when two only of its sides Fig ... Page 19

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**quadrilateral**is equal to two right angles multiplied by 4-2 , which makes four right angles ; therefore , if all the angles of a**quadrilateral**are equal , each of them will be a right angle , which justifies the definition of a square ... Page 20

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**quadrilateral**ABCD ( fig . 44 ) , the opposite sides are equal , namely , AB = CD , and AD = CB , the equal sides will be parallel , and the figure will be a parallelogram . Demonstration . Draw the diagonal BD ; the two triangles ABD ... Page 21

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**quadrilateral**ABCD is a 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 ... Page 34

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**quadrilateral**ABCD are together equal to two right angles ; for the angle BAD has for its measure the half of the arc BCD , and the angle BCD has for its measure the half of the arc BAD ; hence the two angles BAD , BCD , taken together ...### 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