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 36
1. ) side is opposite to the greater angle , the side EG is greater than the side EF ; but EG is equal to BC ; and therefore also BC is greater than EF . There fore , if two triangles , & c . Q. E. D. . PROP . XXV . THEOR .
1. ) side is opposite to the greater angle , the side EG is greater than the side EF ; but EG is equal to BC ; and therefore also BC is greater than EF . There fore , if two triangles , & c . Q. E. D. . PROP . XXV . THEOR .
Página 42
to two right angles ; therefore all the interior , together with all the exterior angles of the figure , are equal to twice as many right angles as there are sides of the figure ; that is , by the fore- D B going corollary , they are ...
to two right angles ; therefore all the interior , together with all the exterior angles of the figure , are equal to twice as many right angles as there are sides of the figure ; that is , by the fore- D B going corollary , they are ...
Página 45
B fore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. 2 PROP . XLII . PROB , To describe a parallelogram that shall be equal to a given triangle , and have one of its angles equal to a given ...
B fore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. 2 PROP . XLII . PROB , To describe a parallelogram that shall be equal to a given triangle , and have one of its angles equal to a given ...
Página 47
of the triangle ABC , because the diameter AC divides it into two equal parts ; whereB fore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. PROP . XLII . PROB , To describe a parallelogram that ...
of the triangle ABC , because the diameter AC divides it into two equal parts ; whereB fore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. PROP . XLII . PROB , To describe a parallelogram that ...
Página 54
BC AB BC ; and AE = AB . Therefore AB.AC + AB.BC = AB2 . There . fore , if a straight line , & c . Q. E D. D TE AB ; PROP . ú . THEOR . . 1 If a 54 ELEMENTS.
BC AB BC ; and AE = AB . Therefore AB.AC + AB.BC = AB2 . There . fore , if a straight line , & c . Q. E D. D TE AB ; PROP . ú . THEOR . . 1 If a 54 ELEMENTS.
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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 |