Elements of Geometry and Trigonometry |
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Page 28
... reason be perpen - C dicular to CD . Hence AB and CD are . perpendicular to the same straight line ; hence they are parallel ( Prop . XVIII . ) . A R Q P F A A PROPOSITION XXIII . THEOREM . Two parallels are every where equally distant ...
... reason be perpen - C dicular to CD . Hence AB and CD are . perpendicular to the same straight line ; hence they are parallel ( Prop . XVIII . ) . A R Q P F A A PROPOSITION XXIII . THEOREM . Two parallels are every where equally distant ...
Page 33
... reason AB is parallel to CD therefore the quadrilateral ABCD is a parallelogram . PROPOSITION XXX . THEOREM . If two opposite sides of a quadrilateral are equal and parallel , the remaining sides will also be equal and parallel , and ...
... reason AB is parallel to CD therefore the quadrilateral ABCD is a parallelogram . PROPOSITION XXX . THEOREM . If two opposite sides of a quadrilateral are equal and parallel , the remaining sides will also be equal and parallel , and ...
Page 46
... reason ; therefore , it would be in both the lines DE , FG . But two straight lines cannot cut each other in more than one point ; hence there is but one circumference which can pass through three given points . Cor . Two circumferences ...
... reason ; therefore , it would be in both the lines DE , FG . But two straight lines cannot cut each other in more than one point ; hence there is but one circumference which can pass through three given points . Cor . Two circumferences ...
Page 53
... reasons . At all events , if the measurement of angles by arcs of a circle is in any degree indirect , it is still equally easy to obtain the direct and absolute measure by this method ; since , on comparing the arc which serves as a ...
... reasons . At all events , if the measurement of angles by arcs of a circle is in any degree indirect , it is still equally easy to obtain the direct and absolute measure by this method ; since , on comparing the arc which serves as a ...
Page 54
... reason , the angle CAD will be measured by the half of ED ; hence BAC + CAD , or BAD will be measured by half of BE + ED , or of BED . Suppose , in the second place , that the centre C lies without the angle BAD . Then drawing the ...
... reason , the angle CAD will be measured by the half of ED ; hence BAC + CAD , or BAD will be measured by half of BE + ED , or of BED . Suppose , in the second place , that the centre C lies without the angle BAD . Then drawing 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.