Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement ... to which are Added, Elements of Plane and Sphericale Trigonometry ... From the Last London Ed., EnlJ.B. Lippincott & Company, 1866 - 317 Seiten |
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Seite 17
... bisect a given rectilineal angle , that is , to divide it into two equal angles A Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut ( 3. 1. ) off AE equal to AD ; join DE ...
... bisect a given rectilineal angle , that is , to divide it into two equal angles A Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut ( 3. 1. ) off AE equal to AD ; join DE ...
Seite 18
... bisect ( 10. 1. ) FG in H , and join CF , CH , CG ; the straight line CH , drawn from the given point C , is per- pendicular to the given straight line AB . C E A F H G B D Because FH is equal to HG , and HC common to the two triangles ...
... bisect ( 10. 1. ) FG in H , and join CF , CH , CG ; the straight line CH , drawn from the given point C , is per- pendicular to the given straight line AB . C E A F H G B D Because FH is equal to HG , and HC common to the two triangles ...
Seite 20
... Bisect ( 10. 1. ) AC in E , join BE and produce it to F , and make Er equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to . CE , EF , each to each ; and the angle AEB is ...
... Bisect ( 10. 1. ) AC in E , join BE and produce it to F , and make Er equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to . CE , EF , each to each ; and the angle AEB is ...
Seite 21
... bisected , it may be demonstrated that the angle BCG , that is ( 15. 1. ) , the angle ACD , is greater than the angle ABC . B E F PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles . Let ABC be ...
... bisected , it may be demonstrated that the angle BCG , that is ( 15. 1. ) , the angle ACD , is greater than the angle ABC . B E F PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles . Let ABC be ...
Seite 37
... Bisect ( 10. 1. ) BC in E , join AE , and at the point E in the straight line EC make ( 23. 1. ) the angle CEF equal to D ; and through A draw ( 31 . 1. ) AG parallel to BC , and through C draw CG ( 31. 1. ) parallel to EF ; Therefore ...
... Bisect ( 10. 1. ) BC in E , join AE , and at the point E in the straight line EC make ( 23. 1. ) the angle CEF equal to D ; and through A draw ( 31 . 1. ) AG parallel to BC , and through C draw CG ( 31. 1. ) parallel to EF ; Therefore ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore