Elements of Plane and Spherical Trigonometry: With Practical Applications |
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Page 18
... side A B be equal to the side DE , the side A C to the side D F , and the angle A to the angle D ; B ÄÄ CE4 then the triangles ABC , DEF will be equal . F Conceive the triangle ABC to be applied to the triangle DEF , so that the side ...
... side A B be equal to the side DE , the side A C to the side D F , and the angle A to the angle D ; B ÄÄ CE4 then the triangles ABC , DEF will be equal . F Conceive the triangle ABC to be applied to the triangle DEF , so that the side ...
Page 19
... side B4 BC to the side EF ; Α D C E4 F then the triangles A B C , DEF will be equal . Conceive the triangle A B C to ... AB is equal to the side AC ; then will the angle B be equal to the angle C. Conceive the angle BAC to be bisect- ed ...
... side B4 BC to the side EF ; Α D C E4 F then the triangles A B C , DEF will be equal . Conceive the triangle A B C to ... AB is equal to the side AC ; then will the angle B be equal to the angle C. Conceive the angle BAC to be bisect- ed ...
Page 20
... sides are also equal , and the triangle is isosceles . Let ABC be a triangle having the an- gle B equal to the angle C ; then will the side A B be equal to the side A C. B D C For , if the two sides are not equal , one of them must be ...
... sides are also equal , and the triangle is isosceles . Let ABC be a triangle having the an- gle B equal to the angle C ; then will the side A B be equal to the side A C. B D C For , if the two sides are not equal , one of them must be ...
Page 21
... side , as AB , is less than the sum of the other two sides , A C and CB . A C B For the straight line AB is the shortest line that can be drawn from the point A to the point B ( Art . 34 , Ax . 10 ) ; hence the side AB is less than the ...
... side , as AB , is less than the sum of the other two sides , A C and CB . A C B For the straight line AB is the shortest line that can be drawn from the point A to the point B ( Art . 34 , Ax . 10 ) ; hence the side AB is less than the ...
Page 22
... AB ; therefore the side A B is greater than A C. 65. Cor . 1. Therefore the shorter side is opposite to the less angle . 66. Cor . 2. In the right - angled triangle the hypothe- Luse is the longest side . PROPOSITION XI . - THEOREM . 6 ...
... AB ; therefore the side A B is greater than A C. 65. Cor . 1. Therefore the shorter side is opposite to the less angle . 66. Cor . 2. In the right - angled triangle the hypothe- Luse is the longest side . PROPOSITION XI . - THEOREM . 6 ...
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Common terms and phrases
A B C ABCD adjacent angles altitude angles ACD angles equal base bisect centre chord circle circumference cone convex surface cosec cosine Cotang diagonal diameter distance divided drawn equal angles equal Prop equiangular equilateral equivalent exterior angle feet four right angles frustum gles greater half the sum homologous homologous sides hypothenuse inches included angle inscribed less Let ABC line A B logarithm mean proportional multiplied parallelogram parallelopipedon perimeter perpendicular polyedron prism PROPOSITION pyramid quadrilateral radii radius ratio rectangle regular polygon right angles Prop right-angled triangle Scholium secant secant line segment side A B side BC similar slant height solidity solve the triangle sphere spherical triangle Tang tangent THEOREM triangle ABC trigonometric functions vertex
Popular passages
Page 17 - 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 57 - 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 155 - The convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude (Prop.
Page 28 - 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 118 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Page 98 - 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 144 - The convex surface of this prism is equal to the perimeter of its base multiplied by its altitude, AG (Prop.
Page 176 - Find the area of the sector having' the same arc with the segment, and also the area of the triangle formed by the chord of the segment and the radii of the sector. Then...
Page 14 - Straight lines which are parallel to the same line are parallel to each other. Let the straight lines AB, CD be each parallel to the line EF ; then are they parallel to each other.
Page 95 - STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.