## Elements of Geometry and Trigonometry |

### From inside the book

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**vertices**of two angles not adjacent . DEFINITIONS OF TERMS . 1. An axiom is a self - evident truth . 2. A demonstration is a train of logical arguments brought to a conclusion . 3. A theorem is a truth which becomes evident by means of ... Page 58

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**vertices**of its three angles in the circumference . And generally , a polygon is said to be inscribed in a circle , when the**vertices**of all the angles are in the circumfer- ence . The circumference of the circle is then said to ... Page 103

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**vertices**B and C in a line paral- lel to the base : and therefore , we have ( B. II . , P. 4 , C. ) AD : DB :: AE : EC . Cor . 1. Hence , by composition , we have ( B. II . , P. 6 ) , AD + DB : AD :: AE + EC : AE , or AB : AD :: AC : AE ... Page 104

... hence , they have the same altitude ( P. 6 , c . ) ; and consequently , their

... hence , they have the same altitude ( P. 6 , c . ) ; and consequently , their

**vertices**D and E lie in a parallel to the base BC ( B. I. , P. 23 ) . PROPOSITION XVII . THEOREM . The line which bisects the 104 GEOMETRY . Page 128

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**vertices**D and F , are situated in a line DF parallel to the base : these triangles are therefore equivalent ( P. 2 , C. ) Add to each of them the figure AECB , and there will result the polygon AEDCB , equivalent to the polygon AFCB ...### Other editions - View all

Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |

### Common terms and phrases

adjacent angles altitude angle ACB angle BAD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cosē Cosine Cosine D Cotang cylinder diagonal diameter distance divided draw drawn equations equivalent feet figure find the area frustum given angle given line gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sinē sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices ΙΟ

### 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...