## 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 T 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

... 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

... 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 66 GEOMETRY .### Other editions - View all

### Common terms and phrases

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