## An Elementary Geometry and Trigonometry |

### From inside the book

Page 30

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**consequent**as the**sum of all the antecedents is to the sum of all the consequents**.**Let**Now and by ( 12 ) and also Adding ( A ) , (**B**) , (**C**) Hence , by ( 14 ) a :**bc**: de : f ab = ab ( A ) ad**bc**(**B**) af be (**C**) - a (**b**+ d + f ) =**b**( ...### Other editions - View all

### Common terms and phrases

A B C ABCDEF acute angle adjacent altitude angle BCD apothem arc or angle bisect centre chord circumference comp cone construct the triangle convex surface Corollary cosec decr diagonals diameter distance divided draw equiangular equilateral equivalent feet Find the Log frustum Geom given angle given line given point given side hypothenuse included angle incr inscribed internal angles isosceles triangle lines A B Logarithm M.
M. Sine multiplied number of sides opposite side parallelogram parallelopiped perimeter perpendicular PLANE GEOMETRY plane triangle PLANE TRIGONOMETRY prism PROBLEM quadrilateral radii radius ratio rectangle regular polygon right angle right pyramid right triangle right-angled triangle Scholium secant segment side opposite similar triangles slant height sphere square straight line Tang tangent THEOREM THEOREM VII trapezoid triangle ABC TRIGONOMETRY vertex

### Popular passages

Page 30 - Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 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...

Page 49 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.

Page 96 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.

Page 12 - In an isosceles triangle the angles opposite the equal sides are equal.

Page 11 - 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 are equal in all respects.

Page 23 - If two triangles have two sides of one respectively equal to two sides of the other, and the angles contained by those sides supplementary, the triangles are equal in area.

Page 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.

Page 71 - The convex surface of a right prism is equal to the perimeter of its base multiplied by its altitude.

Page 40 - At a point 200 feet from, and on a level with the base of a tower, the angle of elevation of the top of the tower is observed to be 60° : what is the height of the tower?

Page 23 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.