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 Trigonometry |
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Página 31
If one side of a triangle be produced , the exterior angle is greater than either of the 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 ...
If one side of a triangle be produced , the exterior angle is greater than either of the 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 ...
Página 32
then the interior and opposite angle ABC ; to each of these add the angle ACB ; therefore the apgles ACD , ACB are greater than the angles ABC , B ACB ; but ACD , ACB are toC D gether equal ( 13. 1 ) to two right angles ; therefore the ...
then the interior and opposite angle ABC ; to each of these add the angle ACB ; therefore the apgles ACD , ACB are greater than the angles ABC , B ACB ; but ACD , ACB are toC D gether equal ( 13. 1 ) to two right angles ; therefore the ...
Página 34
is greater than the 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 ...
is greater than the 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 ...
Página 38
... but EFD is equal to the angle BCA ; therefore also the angle BHA is equal to the angle BCA , that is , the exterior angle BHA of the triangle AHC is equal to its interior and opposite angle BCA : which is impossible ( 16. 1. ) ...
... but EFD is equal to the angle BCA ; therefore also the angle BHA is equal to the angle BCA , that is , the exterior angle BHA of the triangle AHC is equal to its interior and opposite angle BCA : which is impossible ( 16. 1. ) ...
Página 39
than the interior and oppo site angle EFG ; but it is also equal to it , which is impossible therefore , AB Α . E B and CD beiog produced , do not meet towards B , D. In like mannerit may 6 be demonstrated that they с F D do not meet ...
than the interior and oppo site angle EFG ; but it is also equal to it , which is impossible therefore , AB Α . E B and CD beiog produced , do not meet towards B , D. In like mannerit may 6 be demonstrated that they с F D do not meet ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior angle extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportionals proposition proved radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole
Información bibliográfica
| Título | 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 Trigonometry |
| Autor | John Playfair |
| Editor | E. Duyckinck, and George Long, 1824 |
| Procedencia del original | Universidad de Indiana |
| Digitalizado | 15 Ene. 2009 |
| Largo | 333 páginas |
| Exportar cita | BiBTeX EndNote RefMan |