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 32
1 ) to two right angles ; therefore the angles ABC , BCA are less than two right angles . In like manner , it way be demonstrated , that BAC , ACB , as also , CAB , ABC , are less than two right angles . Therefore , any two angles ...
1 ) to two right angles ; therefore the angles ABC , BCA are less than two right angles . In like manner , it way be demonstrated , that BAC , ACB , as also , CAB , ABC , are less than two right angles . Therefore , any two angles ...
Página 33
Io the same manner it may be demonstrated , that the sides AB , BC are greater than CA , and BC , CA greater than AB . Therefore any two sides , & c . Q. E. D. PROP . XXI . THEOR . > If from the OF GEOMETRY . BOOK I. 33.
Io the same manner it may be demonstrated , that the sides AB , BC are greater than CA , and BC , CA greater than AB . Therefore any two sides , & c . Q. E. D. PROP . XXI . THEOR . > If from the OF GEOMETRY . BOOK I. 33.
Página 44
In the same manner , it may be demonstrated that no other line but AD is parallel to BC ; AD is therefore parallel to it . Wherefore B equal triangles upon , & c . Q. E , D. · PROP . XL . THEOR . Equal triangles on the 46 ELEMENTS.
In the same manner , it may be demonstrated that no other line but AD is parallel to BC ; AD is therefore parallel to it . Wherefore B equal triangles upon , & c . Q. E , D. · PROP . XL . THEOR . Equal triangles on the 46 ELEMENTS.
Página 45
... to the triangle GEF , the greater to the less , which is impossible : Therefore AG is not parallel to BF ; and in the same manner it may be demonstrated that there is no other parallel to it but AD ; AD is therefore parallel to BF .
... to the triangle GEF , the greater to the less , which is impossible : Therefore AG is not parallel to BF ; and in the same manner it may be demonstrated that there is no other parallel to it but AD ; AD is therefore parallel to BF .
Página 46
In the same manner , it may be demonstrated that no other line but XD is parallel to BC ; AD is therefore parallel to it . Wherefore B equal triangles upon , & c . Q. E , D. • 1 1 PROP . XL . THEOR . Equal triangles on the 46 ELEMENTS.
In the same manner , it may be demonstrated that no other line but XD is parallel to BC ; AD is therefore parallel to it . Wherefore B equal triangles upon , & c . Q. E , D. • 1 1 PROP . XL . THEOR . Equal triangles on the 46 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 |