Elements of Geometry and Trigonometry |
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Page 10
... intersection A is the vertex of the A4 angle , and the lines AB , AC , are its sides . -B The angle is sometimes designated simply by the letter at the vertex A ; sometimes by the three letters BAC , or CAB , the letter at the vertex ...
... intersection A is the vertex of the A4 angle , and the lines AB , AC , are its sides . -B The angle is sometimes designated simply by the letter at the vertex A ; sometimes by the three letters BAC , or CAB , the letter at the vertex ...
Page 15
... , CB , form one and the same straight line . PROPOSITION IV . THEOREM . When two straight lines intersect each other , the opposite or ver- tical angles , which they form , are equal . Let AB and DE be two straight A lines , BOOK 1 . 15.
... , CB , form one and the same straight line . PROPOSITION IV . THEOREM . When two straight lines intersect each other , the opposite or ver- tical angles , which they form , are equal . Let AB and DE be two straight A lines , BOOK 1 . 15.
Page 16
... intersect each other , are together equal to four right angles : for the sum of the two angles ACE , ECB , is equal to two right angles ; and the sum of the other two , ACD , DCB , is also equal to two right angles : therefore , the sum ...
... intersect each other , are together equal to four right angles : for the sum of the two angles ACE , ECB , is equal to two right angles ; and the sum of the other two , ACD , DCB , is also equal to two right angles : therefore , the sum ...
Page 17
... intersection A : hence , the two triangles EDF , BAC , coincide with each other , and are therefore equal ( Ax . 13. ) . Cor . Whenever , in two triangles , these three things are equal , namely , the angle E = B , the angle F = C , and ...
... intersection A : hence , the two triangles EDF , BAC , coincide with each other , and are therefore equal ( Ax . 13. ) . Cor . Whenever , in two triangles , these three things are equal , namely , the angle E = B , the angle F = C , and ...
Page 49
... intersection , and will divide it into two equal parts . For , let the line AB join the points of intersection . It will be a common chord to the two circles . Now if a perpendicular D be erected from the middle of this chord , it will ...
... intersection , and will divide it into two equal parts . For , let the line AB join the points of intersection . It will be a common chord to the two circles . Now if a perpendicular D be erected from the middle of this chord , it will ...
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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.