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 40
E G the exterior angle EGB is equal to the interior and opposite , upon the same side , GHD ; and the two interior angles BGH , GHD upon the same side are together equal to two right angles . For if AGH be not equal to GHD , let KG be ...
E G the exterior angle EGB is equal to the interior and opposite , upon the same side , GHD ; and the two interior angles BGH , GHD upon the same side are together equal to two right angles . For if AGH be not equal to GHD , let KG be ...
Página 41
THEOR , If a side of any triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles . Let ABC be a triangle , and let one of ...
THEOR , If a side of any triangle be produced , the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles . Let ABC be a triangle , and let one of ...
Página 42
parallel to CE , and BD falls upon them , the exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two ...
parallel to CE , and BD falls upon them , the exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exterior angle ACD is equal to the two ...
Página 49
... line make the interior angles , upon the same side , less than two right angles , do meet if produced ( Cor . 29. 1. ) : Therefore HB , FE will meet , if produced ; let them meet in K , and l througb K draw KL parallel to EA or FH ...
... line make the interior angles , upon the same side , less than two right angles , do meet if produced ( Cor . 29. 1. ) : Therefore HB , FE will meet , if produced ; let them meet in K , and l througb K draw KL parallel to EA or FH ...
Página 55
to the interior and opposite angle ADB ; but ADB is equal ( 5. 1. ) to the angle ABD , because BA is equal to AD , being sides of a square ; H K wherefore the angle CGB is equal to the angle GBC ; and therefore the side BC is equal ( 6.
to the interior and opposite angle ADB ; but ADB is equal ( 5. 1. ) to the angle ABD , because BA is equal to AD , being sides of a square ; H K wherefore the angle CGB is equal to the angle GBC ; and therefore the side BC is equal ( 6.
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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 |