## Elements of Geometry: With, Practical Applications |

### From inside the book

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Page 229

... axis , is a rectangle , and is double of the generating rect- angle ABCD . 2. A

... axis , is a rectangle , and is double of the generating rect- angle ABCD . 2. A

**cone**is a solid , which may be produced by the revolution of a B H K S E C right - angled triangle SAB , conceived to turn about 20 D BOOK EIGHTH. ... Page 230

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**cone**; and the hypothe- nuse SB , its convex surface . The point S is named the vertex of the**cone**; SA , axis or altitude . its Every section HKFI formed at right - angles to the axis , is a circle . Every section SDE passing through ... Page 233

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**cone**, and the sphere , are the three round bodies treated of in the elements of geometry . PROPOSITION I. THEOREM . The solidity of a cylinder is equal to the product of its base by its altitude . Let CA be a radius of the given ... Page 239

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**cone**. Suppose , first , that surf . M N AOXSO is the solidity of a greater**cone**; for example , of the**cone**whose altitude is also SO , but whose base has OB greater than AO for its radius . About the circle whose radius is AO ... Page 240

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**cone**, being contained in it . Hence , first , the base of a**cone**multiplied by a third of its altitude cannot be the measure of a greater**cone**. Neither can this same product be the measure of a smaller**cone**. For now let OB be the ...### Other editions - View all

### Common terms and phrases

a+b+c altitude angle ABC angle BAC angle BCD bisect centre chord circ circular sector circumference circumscribed polygon coincide cone consequently convex surface cylinder denote diagonal diameter dicular distance draw equal and parallel equiangular equilateral triangle equivalent exterior angle figure formed given line greater half the arc hypothenuse inscribed circle intersection isosceles join less Let ABC line AC line CD lines drawn measured by half meet multiplied number of sides parallel planes parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN point G prism PROBLEM produced Prop PROPOSITION pyramid radii radius rectangle regular polygon respectively equal right-angled triangle Sabc Schol Scholium scribed semicircle semicircumference side AC similar similar triangles solid angle sphere spherical triangle square straight line suppose tangent THEOREM three sides triangle ABC triangular prism vertex VIII

### Popular passages

Page 231 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.

Page 147 - PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle : it is required to inscribe a circle in the triangle ABC.

Page 17 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.

Page 28 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...

Page 233 - The volume of a cylinder is equal to the product of its base by its altitude. Let the volume of the cylinder be denoted by V, its base by B, and its altitude by H.

Page 276 - THEOREM. Two triangles on the same sphere, or on equal spheres, are equal in all their parts, when they have each an equal angle included between equal sides. Suppose the side...

Page 120 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.

Page 18 - 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.

Page 232 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.

Page 96 - Similar figures, are those that have all the angles of the one equal to all the angles of the other, each to each, and the sides about the equal angles proportional.