## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |

### From inside the book

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**half**of AF , is less than AE , the**half**of AE + EF . That is , the perpendicular is shorter than any oblique line . Secondly . If we suppose the figure ADB to revolve about AD , the point B will coincide with E , since DB is equal to DE ... Page 22

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**half**of AC + CF , is greater than AE , the**half**of AE + EF . That is , the oblique line terminating farther from the foot of the perpendicular is the longer . Cor . I. The perpendicular measures the shortest distance from a point to ... Page 35

... the parallelogram . THEOREM XXXIII . The straight line joining the middle points of the oblique sides of a trapezoid , will be parallel to the other sides , and equal to

... the parallelogram . THEOREM XXXIII . The straight line joining the middle points of the oblique sides of a trapezoid , will be parallel to the other sides , and equal to

**half**their sum . E A D C H G F B Suppose EF FIRST BOOK . 35. Page 36

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**half**of AD , but ED is also**half**of AD , hence FG and ED are equal and parallel , and the figure EFGD is a parallelogram , and EF is parallel to DC , and also to AB , since DC and AB are parallel . = Again , since EF = DG = AH ; and ... Page 37

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**half**side , the angle will be acute . III . When this line is less than the**half**side , the angle will be obtuse . In the triangle ABC , suppose the line CD to be drawn from the angle C to the middle of the side AB . A D B First ...### Other editions - View all

### Common terms and phrases

a+b+c ACē altitude angles equal apothem bisect centre chord circ circumference cone consequently corresponding cosec Cosine Cotang cylinder decimal denote described diameter dicular distance divided draw drawn equation equivalent exterior angles feet figure formed frustum give given line greater half hence homologous sides hypotenuse inscribed circle intersection logarithm measure middle point multiplied number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right-angled triangle Scholium secant sector similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang tangent THEOREM three sides triangle ABC triangular prism vertex volume