Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added Elements of Plane and Spherical TrigonometryW. E. Dean, 1851 - 317 σελίδες |
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Σελίδα 20
... interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the ex- terior angle ACD is greater than either of the interior opposite angles СВА , ВАС . Bisect ( 10. 1. ) AC in E , join BE and produce ...
... interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the ex- terior angle ACD is greater than either of the interior opposite angles СВА , ВАС . Bisect ( 10. 1. ) AC in E , join BE and produce ...
Σελίδα 21
... interior and opposite angle ABC ; to each of these add the angle ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are to- B gether equal ( 13. 1. ) to two right an- C D gles therefore the angles ...
... interior and opposite angle ABC ; to each of these add the angle ACB ; therefore the angles ACD , ACB are greater than the angles ABC , ACB ; but ACD , ACB are to- B gether equal ( 13. 1. ) to two right an- C D gles therefore the angles ...
Σελίδα 23
... interior and opposite angle , the exte- rior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is ...
... interior and opposite angle , the exte- rior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that the angle BDC is ...
Σελίδα 27
... interior and opposite angle BCA , which is impossible ( 16. 1. ) ; wherefore BC is not unequal to EF , that is , it is equal to it ; and AB is equal to DE ; therefore the two , AB , BC are equal to the two DE , EF , each to each ; and ...
... interior and opposite angle BCA , which is impossible ( 16. 1. ) ; wherefore BC is not unequal to EF , that is , it is equal to it ; and AB is equal to DE ; therefore the two , AB , BC are equal to the two DE , EF , each to each ; and ...
Σελίδα 28
... interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles . Let the straight line EF fall upon the parallel straight lines AB , CD ; the alternate angles AGH ...
... interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles . Let the straight line EF fall upon the parallel straight lines AB , CD ; the alternate angles AGH ...
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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 solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore