## Elements of Geometry and Trigonometry |

### From inside the book

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**diagonal**is a line which joins the ver- tices of two angles not adjacent to each other . Thus , AF , AE , AD , AC , are**diagonals**. B E G 19. An equilateral polygon is one which has all its sides . equal ; an equiangular polygon , one ... Page 30

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**diagonals**B AC , AD , AE , AF , be drawn to the vertices of all the opposite angles , it is plain that the poly- gon will be divided into five triangles , if it has seven sides ; into six triangles , if it has eight ; and , in general ... Page 32

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**diagonal**BD . The triangles ABD , DBC , have a common side BD ; and since AD , BC , are parallel , they have also the angle ADB DBC , ( Prop . XX . Cor . 2. ) ; and since AB , CD , are parallel , the angle ABD BDC : hence the two ... Page 33

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**diagonal**DB , dividing the quadrilateral into two triangles . Then , since AB is parallel to DC , the alternate ...**diagonals**of a parallelogram divide each other into equal parts , or mutually bisect each other . Let ABCD be a ... Page 66

... exact number of times in the preceding one . When this happens , the two lines have no common measure , and are said to be incommensurable . An instance of this will be seen after- wards , in the ratio of the

... exact number of times in the preceding one . When this happens , the two lines have no common measure , and are said to be incommensurable . An instance of this will be seen after- wards , in the ratio of the

**diagonal**to the 66 GEOMETRY .### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex