Elements of Geometry and Trigonometry |
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Page 11
... square , which has its sides equal , and its an- gles right - angles . The rectangle , which has its angles right an- gles , without having its sides equal . The parallelogram , or rhomboid , which has its opposite sides parallel . The ...
... square , which has its sides equal , and its an- gles right - angles . The rectangle , which has its angles right an- gles , without having its sides equal . The parallelogram , or rhomboid , which has its opposite sides parallel . The ...
Page 13
... square of the line AB is designated by AB2 ; its cube by AB3 . What is meant by the square and cube of a line , will be explained in its proper place . The sign indicates a root to be extracted ; thus √2 means the square - root of 2 ...
... square of the line AB is designated by AB2 ; its cube by AB3 . What is meant by the square and cube of a line , will be explained in its proper place . The sign indicates a root to be extracted ; thus √2 means the square - root of 2 ...
Page 31
... square . Cor . 2. The sum of the angles of a pentagon is equal to two right angles multiplied by 5-2 , which amounts to six right angles : hence , when a pentagon is equiangular , each angle is equal to the fifth part of six right ...
... square . Cor . 2. The sum of the angles of a pentagon is equal to two right angles multiplied by 5-2 , which amounts to six right angles : hence , when a pentagon is equiangular , each angle is equal to the fifth part of six right ...
Page 36
... square of the mean . PROPOSITION II . THEOREM . If the product of two quantities be equal to the product of two other quantities , two of them will be the extremes and the other two the means of a proportion . Let MxQ = Nx P ; then will ...
... square of the mean . PROPOSITION II . THEOREM . If the product of two quantities be equal to the product of two other quantities , two of them will be the extremes and the other two the means of a proportion . Let MxQ = Nx P ; then will ...
Page 63
... square . PROBLEM XIII . To find the centre of a given circle or arc . Take three points , A , B , C , any where in the circumference , or the arc ; draw AB , BC , or suppose them to be drawn ; bisect those two lines by the ...
... square . PROBLEM XIII . To find the centre of a given circle or arc . Take three points , A , B , C , any where in the circumference , or the arc ; draw AB , BC , or suppose them to be drawn ; bisect those two lines by 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.