## 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 G H F ལའ 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 CG ... 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 . C A D B First ...### Other editions - View all

### Common terms and phrases

a+b+c altitude apothem bisect centre chord circumference circumscribed cone consequently corresponding cosec Cosine Cotang cube cubic cylinder decimal denote diameter dicular divided draw drawn equation equivalent exterior angles feet figure frustum Geom give greater half hence hypotenuse inches intersection logarithm measure multiplied number of sides opposite parallel 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 solve the triangle sphere spherical triangle square straight line subtract suppose surface Tang tangent THEOREM three sides triangle ABC triangular prism volume ΙΟ

### Popular passages

Page 35 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

Page 80 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.

Page 139 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.

Page 17 - The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two.

Page 176 - The radius of a sphere is a straight line, drawn from the centre to any point of the...

Page 182 - Every section of a sphere, made by a plane, is a circle.

Page 28 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C ' with Proof STATEMENTS Apply A A'B'C ' to A ABC so that A'B

Page 165 - ... bases simply : hence two prisms of the same altitude are to each other as their bases. For a like reason, two prisms of the same base are to each other as their altitudes.

Page 29 - ... to two sides of the other, but the third side of the first greater than the third side of the second, the angle opposite the third side of the first is.

Page 13 - If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another.