## Elements of Geometry and Trigonometry |

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ABCD altitude base called centre chord circle circumference circumscribed common comp cone consequently contained convex surface corresponding Cosine Cotang cylinder described determine diagonal diameter difference distance divided draw drawn edges equal equations equivalent example expressed extremity faces fall feet figure follows formed four frustum given greater half height hence homologous hypothenuse included inscribed intersect length less logarithm magnitudes manner means measured meet middle multiplied opposite parallel parallelogram pass perimeter perpendicular plane polygon prism PROBLEM proportional PROPOSITION pyramid radii radius ratio reason rectangle regular remaining right angles right-angled triangle Scholium segment sides similar sine solidity sphere square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex vertices whole

### Popular passages

Page 24 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.

Page 38 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

Page 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.

Page 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...

Page 43 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the sum of the exterior angles.

Page 215 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.

Page 107 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.

Page 93 - The area of a parallelogram is equal to the product of its base and altitude.

Page 231 - The angles of spherical triangles may be compared together, by means of the arcs of great circles described from their vertices as poles and included between their sides : hence it is easy to make an angle of this kind equal to a given angle.

Page 232 - F, be respectively poles of the sides BC, AC, AB. For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...