Elements of Geometry and Trigonometry |
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Page 2
... manner , the properties of num- bers , and the best rules for their various applications . DAVIES ' BOURDON'S ALGEBRA - Being an abridg ment of the work of M. Bourdon , with the additions of practical examples . DAVIES ' LEGENDRE'S ...
... manner , the properties of num- bers , and the best rules for their various applications . DAVIES ' BOURDON'S ALGEBRA - Being an abridg ment of the work of M. Bourdon , with the additions of practical examples . DAVIES ' LEGENDRE'S ...
Page 4
... manner of treating the subjects of Plane and Spherical Trigonometry . It has also been thought best to publish with the present edition a table of logarithms and logarithmic sines , and to apply the principles of geometry to the ...
... manner of treating the subjects of Plane and Spherical Trigonometry . It has also been thought best to publish with the present edition a table of logarithms and logarithmic sines , and to apply the principles of geometry to the ...
Page 17
... manner , since the angle F is equal to the argle C , the line FD will take the direction CA , and the point D will be found somewhere in the line CA. Hence , the point D , falling at the same time in the two straight lines BA and CA ...
... manner , since the angle F is equal to the argle C , the line FD will take the direction CA , and the point D will be found somewhere in the line CA. Hence , the point D , falling at the same time in the two straight lines BA and CA ...
Page 20
... manner it may be shown that the angle E is equal to B , and the angle F to C : hence the two triangles are equal ( Prop . VI . Sch . ) . Scholium . It may be observed that the equal angles lie op- posite the equal sides : thus , the ...
... manner it may be shown that the angle E is equal to B , and the angle F to C : hence the two triangles are equal ( Prop . VI . Sch . ) . Scholium . It may be observed that the equal angles lie op- posite the equal sides : thus , the ...
Page 27
... manner it may be proved that OGA + GOC is equal to two right angles . Cor . 1. If OGB is a right angle , GOD will be a right angle also therefore , every straight line perpendicular to one of two parallels , is perpendicular to the ...
... manner it may be proved that OGA + GOC is equal to two right angles . Cor . 1. If OGB is a right angle , GOD will be a right angle also therefore , every straight line perpendicular to one of two parallels , is perpendicular to the ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface Cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Popular passages
Page 241 - 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.
Page 19 - 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 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Page 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.