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

### From inside the book

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**similar**, it may be shown that the fourth term of the proportion cannot be less than AD ; therefore it must be AD ; hence we have , Angle A CB : angle A CD :: arc A B : arc A D. 198. Scholium 1. Since the angle at the centre of a circle ... Page 76

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**SIMILAR**FIGURES are such as have the angles of the one equal to those of the other , each to each , and the sides containing the equal angles proportional . 211. EQUIVALENT FIGURES are such as have equal areas . Figures may be ... Page 77

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**similar**to the arc FG ; the segment BDC to the segment FHG , and the sector ABC to the B sector EF G. E A C F G D. II A 214. The ALTITUDE OF A TRIANGLE is the perpendicular , which measures the distance of any one of its vertices from ... Page 99

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**similar**. Let the two triangles ABC , DCE be equiangular ; the angle BAC being equal to the angle CDE , the angle ABC to the angle DCE , and the angle ACB to the angle DEC , then the homologous sides will be B proportional , and we ... Page 100

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**similar**; since the third angles will also be equal , and the two tri- angles be equiangular . 261. Scholium . In**similar**triangles , the homologous sides are opposite to the equal angles ; thus the angle A C B being equal to D E C ...### 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.