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 23
Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AŁ is equal to BC .
Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AŁ is equal to BC .
Página 24
... is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor . def .
... is equal to the angle EDF ; wherefore also the point C shall coincide with the point F , because AC is equal to DF : But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ( cor . def .
Página 25
remainder CG ; and FC was proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3. 1. ) ...
remainder CG ; and FC was proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3. 1. ) ...
Página 26
... angle ECD is greater than the angle BCD ; wherefore А B the angle FDC is likewise greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) ...
... angle ECD is greater than the angle BCD ; wherefore А B the angle FDC is likewise greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) ...
Página 27
to the angle EAF : wherefore the given rectilineal angle BAC is bisected by the straight line AF . E Which was to be done . B PROP . , X . PROB . To bisect a OF GEOMETRY . BOOK I. 27 D ...
to the angle EAF : wherefore the given rectilineal angle BAC is bisected by the straight line AF . E Which was to be done . B PROP . , X . PROB . To bisect a OF GEOMETRY . BOOK I. 27 D ...
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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 |