Elements of Geometry and Trigonometry |
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Page 4
... coincide so nearly , as to differ from each other by less than any assignable quantity , has been taken from the Edinburgh Encyclopedia . It is proved in the corollaries that a polygon of an infinite number of sides becomes a circle ...
... coincide so nearly , as to differ from each other by less than any assignable quantity , has been taken from the Edinburgh Encyclopedia . It is proved in the corollaries that a polygon of an infinite number of sides becomes a circle ...
Page 13
... which shall be parallel to a given line . 13. Magnitudes , which being applied to each other , coincide throughout their whole extent , are equal . PROPOSITION I. THEOREM . If one straight line meet another BOOK I. 13.
... which shall be parallel to a given line . 13. Magnitudes , which being applied to each other , coincide throughout their whole extent , are equal . PROPOSITION I. THEOREM . If one straight line meet another BOOK I. 13.
Page 14
... coincide with each other throughout their whole extent , and form one and the same straight line . Let A and B be the two common points . In the first place it is evident that the two lines must coincide entirely between A and B , for ...
... coincide with each other throughout their whole extent , and form one and the same straight line . Let A and B be the two common points . In the first place it is evident that the two lines must coincide entirely between A and B , for ...
Page 15
... coincide : there- fore , the straight lines which have two points A and B com- mon , cannot separate at any point , when produced ; hence they form one and the same straight line . PROPOSITION III . THEOREM . If a straight line meet two ...
... coincide : there- fore , the straight lines which have two points A and B com- mon , cannot separate at any point , when produced ; hence they form one and the same straight line . PROPOSITION III . THEOREM . If a straight line meet two ...
Page 16
... coincide . Let the triangle EDF , be placed upon the triangle BAC , so that the point E shall fall upon B , and the side ED on the equal side BA ; then , since the angle D is equal to the angle A , the side DF will take the direction AC ...
... coincide . Let the triangle EDF , be placed upon the triangle BAC , so that the point E shall fall upon B , and the side ED on the equal side BA ; then , since the angle D is equal to the angle A , the side DF will take the direction AC ...
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Common terms and phrases
adjacent altitude angle ACB 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 measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC 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 18 - If two triangles have two sides of the one equal to two sides of the...
Page 213 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 233 - It is, indeed, evident, that the negative characteristic will always be one greater than the number of ciphers between the decimal point and the first significant figure.
Page 287 - How many square feet are there in the convex surface of the frustum of a square pyramid, whose slant height is 10 feet, each side of the lower base 3 feet 4 inches, and each side of the upper base 2 feet 2 inches ? Ans.
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'.