Elements of Geometry and Trigonometry |
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Page 16
... straight line DE is met by the straight line AC , the sum of the angles ACE , ACD , is equal to two right angles ( Prop . I. ) ; and since the straight line AB , is met by the straight line EC , the sum of the angles ACE and ECB , is ...
... straight line DE is met by the straight line AC , the sum of the angles ACE , ACD , is equal to two right angles ( Prop . I. ) ; and since the straight line AB , is met by the straight line EC , the sum of the angles ACE and ECB , is ...
Page 17
... line BA . In like manner , since the angle F is equal to the angle C , the line FD will take the direction CA , and the point D will be found somewhere in the line CA. Hence , the point D , falling at the same time in the two straight lines ...
... line BA . In like manner , since the angle F is equal to the angle C , the line FD will take the direction CA , and the point D will be found somewhere in the line CA. Hence , the point D , falling at the same time in the two straight lines ...
Page 18
... line AB is the shortest dis- tance between the points A and B ( Def . 3. ) ; hence AC + CB is greater than AB . B PROPOSITION VIII . THEOREM . If from any point within a triangle , two straight lines be drawn to the extremities of ...
... line AB is the shortest dis- tance between the points A and B ( Def . 3. ) ; hence AC + CB is greater than AB . B PROPOSITION VIII . THEOREM . If from any point within a triangle , two straight lines be drawn to the extremities of ...
Page 19
... straight line GC < GI + IC , and the straight line AB < AI + IB ; therefore , GC + AB < GI + AI + IC + IB , or , which is the same thing , GC + AB AG + BC . Take away AB from the one side , and its equal AG from the other ; and there ...
... straight line GC < GI + IC , and the straight line AB < AI + IB ; therefore , GC + AB < GI + AI + IC + IB , or , which is the same thing , GC + AB AG + BC . Take away AB from the one side , and its equal AG from the other ; and there ...
Page 22
... straight line , only one perpendicu- lar can be drawn to that line . Let A be the point , and DE the given line .. B Let us suppose that we can draw two perpendiculars , AB , AC . Produce either of them , as AB , till BF is equal to AB ...
... straight line , only one perpendicu- lar can be drawn to that line . Let A be the point , and DE the given line .. B Let us suppose that we can draw two perpendiculars , AB , AC . Produce either of them , as AB , till BF is equal to AB ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex