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 32
Let ABC be any triangle ; any A two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ACD is greater ( 16. 1. ) then the interior and opposite angle ABC ...
Let ABC be any triangle ; any A two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ACD is greater ( 16. 1. ) then the interior and opposite angle ABC ...
Página 33
For , if it be not greater , AC must A either be equal to AB , or less than it ; it is not equal , because then the angle ABC would be equal ( ö . 1. ) to the angle ACB ; but it is not ; therefore AC is not equal to AB ; neither is it 3 ...
For , if it be not greater , AC must A either be equal to AB , or less than it ; it is not equal , because then the angle ABC would be equal ( ö . 1. ) to the angle ACB ; but it is not ; therefore AC is not equal to AB ; neither is it 3 ...
Página 34
If from the ends of one side of a triangle , there be drawn two straight lines to a point within the triangle , these two lines shall be less than the other two sides of the triangle , but shall contain a greater angle .
If from the ends of one side of a triangle , there be drawn two straight lines to a point within the triangle , these two lines shall be less than the other two sides of the triangle , but shall contain a greater angle .
Página 37
For , if it be not greater , it must either be equal to it , or less ; but the angle BAC is not equal to the angle EDF , because then the base BC would be equal ( 4. 1. ) A D to EF ; but it is not ; therefore the angle BAC is not equal ...
For , if it be not greater , it must either be equal to it , or less ; but the angle BAC is not equal to the angle EDF , because then the base BC would be equal ( 4. 1. ) A D to EF ; but it is not ; therefore the angle BAC is not equal ...
Página 38
... therefore the angle GCB is equal to the angle DFE but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the angle BCG is equal to the angle BCA , the less to the greater , which is impossible ; therefore AB is not ...
... therefore the angle GCB is equal to the angle DFE but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the angle BCG is equal to the angle BCA , the less to the greater , which is impossible ; therefore AB is not ...
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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 |