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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
Dentro del libro
Página 124
... altitude of any figure is the straight line drawn from its vertex perpendicular to the base , PROP . I. THEOR . Triangles and parallelograms , of the same altitude , are one to another as their bases . Let the triangles ABC , ACD , and ...
... altitude of any figure is the straight line drawn from its vertex perpendicular to the base , PROP . I. THEOR . Triangles and parallelograms , of the same altitude , are one to another as their bases . Let the triangles ABC , ACD , and ...
Página 125
... 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 the vertices of the triangles to the bases , the straight line which ...
... 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 the vertices of the triangles to the bases , the straight line which ...
Página 126
... altitude , viz . the perpen- dicular 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 tri- angle ADE , so is CE to EA . Therefore , as BD to DA , so is CE to EA ...
... altitude , viz . the perpen- dicular 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 tri- angle ADE , so is CE to EA . Therefore , as BD to DA , so is CE to EA ...
Página 136
... 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 equal angles are reci- procally proportional . But ...
... 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 equal angles are reci- procally proportional . But ...
Página 171
... altitudes are as their bases ( 1. 6. ) , X :: AO :: Y : GP , and again alternately , X : Y :: AO : GP ; wherefore , taking the doubles of each , the circumfer- ence ABD is to the circumference GHL as the diameter AD to the diameter GL ...
... altitudes are as their bases ( 1. 6. ) , X :: AO :: Y : GP , and again alternately , X : Y :: AO : GP ; wherefore , taking the doubles of each , the circumfer- ence ABD is to the circumference GHL as the diameter AD to the diameter GL ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
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 |