## 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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**Theorems**+ Definitions ...**Theorems**.. • · Definitions .**Theorems**.. FIFTH BOOK . 137 138 SIXTH BOOK . 152 154 SEVENTH BOOK . 174 177 EIGHTH BOOK . Definitions**Theorems**191 192 Regular polyedrons ... 208 Application of Algebra to the ... Page 12

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**theorem**is a proposition which requires a demonstra- tion . VI . A corollary is an immediate consequence of one or more propositions . If any new course of reasoning is required to establish it , this reasoning is so simple that it may ... Page 14

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**THEOREM**I. When a straight line meets or crosses another , the adjacent angles are supplements ; and the opposite ...**Theorem**. F 12 E C D -B Cor . III . 14 GEOMETRY .**THEOREMS**Of angles. Page 15

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**THEOREM**II . If through the vertex of any angle , lines are drawn perpen- dicular respectively to its sides , they will form a new angle , either equal to the first , or supplementary to it . Let BAC be the given angle , DE perpendic ... Page 18

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**THEOREM**VI . The exterior angle , formed by producing one of the sides of a triangle , is equal to the sum of the two interior and opposite angles of the triangle . In the triangle ABC , if the side AB be pro- duced to D , the exterior ...### 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.