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 124
The altitude of any figure is the straight line drawn from its vertex perpendicular to the base , PROP . I. THEOR .臺 Triangles and parallelograms , of the same altitude , are one to another as their bases .
The altitude of any figure is the straight line drawn from its vertex perpendicular to the base , PROP . I. THEOR .臺 Triangles and parallelograms , of the same altitude , are one to another as their bases .
Página 125
From this it is plain , that triangles and parallelograms that have equal altitudes , are to one another as their bases . Let the figures be placed so as to have their bases in the same straight line ; and having drawn perpendiculars ...
From this it is plain , that triangles and parallelograms that have equal altitudes , are to one another as their bases . Let the figures be placed so as to have their bases in the same straight line ; and having drawn perpendiculars ...
Página 126
BD to DA , because having the same altitude , viz . the perpendicular drawn from the point E to AB , they are to one another as their bases ; and for the same reason , as the triangle CDE to the triangle ADE , so is CE to EA .
BD to DA , because having the same altitude , viz . the perpendicular drawn from the point E to AB , they are to one another as their bases ; and for the same reason , as the triangle CDE to the triangle ADE , so is CE to EA .
Página 136
but because the parallelograms AB , FE have the same altitude , AB : FE :: DB : BE ( 1. 6. ) , also , BC : FE :: GB : BF ( 1.6 ) ; therefore DB : BE :: GB : BF ( 11. 5. ) . Wherefore , the sides of the parallelograms AB , BC about their ...
but because the parallelograms AB , FE have the same altitude , AB : FE :: DB : BE ( 1. 6. ) , also , BC : FE :: GB : BF ( 1.6 ) ; therefore DB : BE :: GB : BF ( 11. 5. ) . Wherefore , the sides of the parallelograms AB , BC about their ...
Página 171
Y ; : GP2 ; whence , because rectangles that have equal altitudes are as their bases ( 1. 6. ) , X :: A0 :: Y : GP , and again alternately , X : Y :: A0 : GP ; wherefore , taking the doubles of each , the circumference ABD is to the ...
Y ; : GP2 ; whence , because rectangles that have equal altitudes are as their bases ( 1. 6. ) , X :: A0 :: Y : GP , and again alternately , X : Y :: A0 : GP ; wherefore , taking the doubles of each , the circumference ABD is to the ...
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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 |