## Elements of Plane and Spherical Trigonometry: With Practical Applications |

### From inside the book

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**Prop**. I. Cor . 1 ) ; and since ACE is a straight line , the angle FCE will also be a right angle ; therefore the angle FCE is**equal**to the angle FCD ( Art . 34 , Ax . 13 ) , a part to the whole , which is impossible ; hence two ... Page 20

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**equal**to the angle C (**Prop**. V. ) . B 57. Cor . 1. The line bisecting the vertical angle of an isosceles triangle bisects the base at right angles . 58. Cor . 2. Conversely , the line bisecting the base of an isosceles triangle at ... Page 22

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**equal**to it or less . If the angle C were**equal**to B , then would the side A B be**equal**to the side A C (**Prop**... (**Prop**. X. Cor . 1 ) , which is also contrary to the hypothesis . Hence , the angle C must be greater than B. 68. Cor . It ... Page 24

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**equal**to the angle BCA (**Prop**. V. ) But the angle BCA is , by hypothesis , a right angle ; therefore BCF must also be a right angle ; and if the two adja- cent angles , BCA and BCF , are to- gether**equal**to two right angles , the two ... Page 25

... ( Prop . I. Cor . 1 ) ; hence the third sides , CF and A C , are

... ( Prop . I. Cor . 1 ) ; hence the third sides , CF and A C , are

**equal**(**Prop**. V. Cor . ) . But ABF , being a straight line , is shorter than ACF , which is a broken line ( Art . 34 , Ax . 10 ) ; therefore AB , the half of ABF , is ...### Other editions - View all

### Common terms and phrases

A B C ABCD adjacent angles altitude angle ACB angle equal base bisect centre chord circle circumference circumscribed cone convex surface cosec Cosine Cotang cylinder diagonal diameter distance divided drawn equal Prop equilateral triangle equivalent exterior angle feet formed frustum gles greater half the sum hence homologous hypothenuse inches included angle inscribed interior angles isosceles less Let ABC line A B logarithmic sine measured by half multiplied number of sides parallel parallelogram parallelopipedon pendicular perimeter perpendicular polyedron prism PROBLEM PROPOSITION pyramid quadrantal radii radius ratio rectangle regular polygon Required the area right angles right-angled triangle rods Scholium secant segment side A B similar slant height solve the triangle sphere spherical polygon spherical triangle Tang tangent THEOREM triangle ABC triangle equal trigonometric functions vertex

### Popular passages

Page 28 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

Page 37 - 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 79 - Two rectangles having equal altitudes are to each other as their bases.

Page 251 - The convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude (Prop.

Page 52 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.

Page 35 - If any side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles.

Page 168 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.

Page 303 - Equal triangles upon the same base, and upon the same side of it, are between the same parallels.

Page 4 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a"" . Therefore, log (M m) = xm = (log M) X »»12.

Page 102 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing.