## Elements of Geometry and Trigonometry |

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ABCD altitude base Book called centre chord circle circumference circumscribed coincide common cone consequently construct corresponding Cosine Cotang cylinder denote described diameter difference distance divided draw drawn edges equal EXAMPLES extremity faces feet figure formed Formula four frustum given greater half height hence homologous included inscribed intersection length less logarithm lower base manner mean measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular placed plane polyedron polygon position principle prism proportional PROPOSITION proved pyramid radii radius rectangle regular result right angles RULE Scholium segment shown sides similar Sine solution sphere spherical triangle square straight line surface taken Tang tangent term THEOREM third triangle triangle ABC unit vertex vertices volume whence

### Popular passages

Page 26 - 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 in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.

Page 57 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.

Page 124 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.

Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 102 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.

Page 44 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 41 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 57 - A chord is a straight line joining the extremities of an arc.

Page 16 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, etc.

Page 55 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.