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 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
The case in which the vertex of one triangle is upon a side of the other , Deeds no demonstration . Therefore , upon the same base , and on the same side of it , there cannot be two triangles that have their sides wbich are terminated ...
The case in which the vertex of one triangle is upon a side of the other , Deeds no demonstration . Therefore , upon the same base , and on the same side of it , there cannot be two triangles that have their sides wbich are terminated ...
Página 27
... the base equal to one another , and likewise their sides terminated in the other extremity ; but this is impossible ( 7. 1. ) ; therefore , if the base BC coincides with the base EF , the sides BA , AC cannot but coincide with the ...
... the base equal to one another , and likewise their sides terminated in the other extremity ; but this is impossible ( 7. 1. ) ; therefore , if the base BC coincides with the base EF , the sides BA , AC cannot but coincide with the ...
Página 30
If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines are in one and the same straight line .
If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines are in one and the same straight line .
Página 32
Therefore if one side , & c . Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any A two of its angles together are less than two right angles .
Therefore if one side , & c . Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any A two of its angles together are less than two right angles .
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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 |