## Elements of Geometry: With Practical Applications ... |

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ABCD altitude base bisect called centre chord circ circle circumference circumscribed coincide common cone consequently construction contained convex corresponding cylinder denote described diagonal diameter difference distance divided double draw equal equilateral equivalent exterior angle extremities figure follows formed four given gives greater hence included inscribed intersection join less lines drawn magnitude manner mean measured measured by half meet multiplied opposite parallel parallel planes parallelogram parallelopipedon pass perimeter perpendicular plane plane MN polygon portion prism PROBLEM produced Prop proportional PROPOSITION pyramid radii radius ratio rectangle regular polygon remain respectively right angles sector segment shown sides similar solid solid angle sphere spherical square straight line suppose surface taken tangent THEOREM third triangle ABC vertex VIII whole

### Popular passages

Page 37 - 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 180 - THEOREM. If one of two parallel lines is perpendicular to a plane, the other will also be perpendicular to this plane. Let AP & ED be parallel lines, of which AP is perpendicular to the plane MN ; then will ED be also perpendicular to this plane.

Page 139 - 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 224 - The radius of a sphere is a straight line, drawn from the centre to any point of the...

Page 43 - In a right-angled triangle, the side opposite the right angle is" called the Hypothenuse ; and the other two sides are cal4ed the Legs, and sometimes the Base and Perpendicular.

Page 184 - THEOREM. If two angles, not situated in the same plane, have their sides parallel and lying in the same direction, they will be equal, and the planes in which they are situated will be parallel.

Page 10 - 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 226 - We conclude then, that the solidity of a cylinder is equal to the product of its base by its altitude.

Page 22 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...

Page 12 - 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.