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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
Dentro del libro
Resultados 1-5 de 30
Página 31
... interior , and opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite an- gles CBA , BAC . 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 exterior angle ACD is greater than either of the interior opposite an- gles CBA , BAC . Bisect ( 10. 1. ) AC in E , join BE and produce ...
Página 32
... 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- gether equal ( 13. 1 ) to two right angles ; therefore the angles ABC ...
... 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- gether equal ( 13. 1 ) to two right angles ; therefore the angles ABC ...
Página 34
... interior and opposite angle , the exterior 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 exterior 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 ...
Página 38
... interior and opposite angle BCA : which is im- possible ( 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 im- possible ( 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 ...
Página 39
... interior and opposite upon the same side of the line ; or makes the interior angles upon the same side together equal to two right angles ; the two straight lines are parallel to one another . Let the straight line EF , which falls upon ...
... interior and opposite upon the same side of the line ; or makes the interior angles upon the same side together equal to two right angles ; the two straight lines are parallel to one another . Let the straight line EF , which falls upon ...
Otras ediciones - Ver todas
Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore