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 xiv
... and particularly to EUCLID , that they have been at great pains to prove the truth of many simple propositions ... is here made to abridge the Elements , by considering as self - evident any thing that admits of being proved .
... and particularly to EUCLID , that they have been at great pains to prove the truth of many simple propositions ... is here made to abridge the Elements , by considering as self - evident any thing that admits of being proved .
Página 22
Definition ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to AB : But it has been proved that CA is equal to AB ; therefore - CA , CB are each of them equal to AB ; now things which are equal to the same ...
Definition ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to AB : But it has been proved that CA is equal to AB ; therefore - CA , CB are each of them equal to AB ; now things which are equal to the same ...
Página 24
... AFC to the TL F G angle AGB : And because the whole AF is equal to the whole AG , and the part AB to the part AC ; the remain- DY 1 der BF shall be equal ( 3. Ax . ) to the > remainder CG ; and FC was proved to be equal 24 ELEMENTS.
... AFC to the TL F G angle AGB : And because the whole AF is equal to the whole AG , and the part AB to the part AC ; the remain- DY 1 der BF shall be equal ( 3. Ax . ) to the > remainder CG ; and FC was proved to be equal 24 ELEMENTS.
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
to the angle BCD ; but BDC has been proved to be greater than the same BCD ; which is impossible . The case in which the vertex of one triangle is upon a side of the other , Deeds no demonstration . Therefore , upon the same base ...
to the angle BCD ; but BDC has been proved to be greater than the same BCD ; which is impossible . The case in which the vertex of one triangle is upon a side of the other , Deeds no demonstration . Therefore , upon the same base ...
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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 |