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 . ) . R T Q D P B 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 . ) . R T Q D P B 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 convex surface cosine cotangent 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 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