## 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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Page 41

... polygon is inscribed in a circle when its sides are inscribed ; and under the same cir- cumstances , the circle is said to circumscribe the polygon . A circle is ...

... polygon is inscribed in a circle when its sides are inscribed ; and under the same cir- cumstances , the circle is said to circumscribe the polygon . A circle is ...

**regular polygon**may have any number of sides not SECOND BOOK . 41. Page 42

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**regular polygon**may have any number of sides not less than three . The equilateral triangle is a**regular polygon**of three sides . The square is also a**regular polygon**of four sides . OF CHORDS , SECANTS , AND TANGENTS . THEOREM I. Every ... Page 54

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**regular polygons**are capable of being inscribed in a circle , and of circumscribing a circle . Let ABCDEF be any**regular polygon**; B A H K and through three consecutive angles A , B , and C , describe the circumference of a circle ( T ... Page 55

... polygon ; hence the angle GCB = GCD . Now , comparing the two triangles GBC and GCD , we have the side GC common ...

... polygon ; hence the angle GCB = GCD . Now , comparing the two triangles GBC and GCD , we have the side GC common ...

**regular polygon**. The radius of the circumscribing circle is called the radius of the polygon , and the radius of ... Page 56

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**regular polygon**, already inscribed in a circle , we draw tangents , we shall thus circumscribe a**regular polygon**of the same number of sides . = A " E ' A ' BU B C1 The tangents thus drawn will form with the sides of the inscribed ...### 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.