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 |
Dentro del libro
Página 23
PROP . III . PROB From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part ...
PROP . III . PROB From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part ...
Página 25
... angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore , the angles at the base , & c . Q. E. D. COROLLARY . Hence every equilateral triangle is also equiangular . PROP . VI . THEOR .
... angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore , the angles at the base , & c . Q. E. D. COROLLARY . Hence every equilateral triangle is also equiangular . PROP . VI . THEOR .
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Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut ( 3. 1. ) ...
Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut ( 3. 1. ) ...
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PROP . , X . PROB . To bisect a given finite straight line , that is , to divide it into two equal parts . > Let AB be the given straight line ; it is required to divide it into two equal parts . Describe ( 1. 1. ) ...
PROP . , X . PROB . To bisect a given finite straight line , that is , to divide it into two equal parts . > Let AB be the given straight line ; it is required to divide it into two equal parts . Describe ( 1. 1. ) ...
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... therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but CBE , EBD , are two right angles ; therefore DBA , ABC are together equal to two right angles . Wherefore , when a straight line , & c . Q. E. D. PROP .
... therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but CBE , EBD , are two right angles ; therefore DBA , ABC are together equal to two right angles . Wherefore , when a straight line , & c . Q. E. D. PROP .
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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 |