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 25
to BD ; and it was shewn to be equal to it . COR . 1. Hence , if two opposite sides of a quadrilateral are equal and parallel , the remaining sides will also be equal and parallel , and the figure will be a parallelogram . COR . 2.
to BD ; and it was shewn to be equal to it . COR . 1. Hence , if two opposite sides of a quadrilateral are equal and parallel , the remaining sides will also be equal and parallel , and the figure will be a parallelogram . COR . 2.
Página 26
... BAC has been shewn to be equal to the angle BDC : therefore the opposite sides and angles of a parallelogram are equal to one another ; also , its diameter bisects it ; for AB being equal to CD , and BC common , the two AB , BC are ...
... BAC has been shewn to be equal to the angle BDC : therefore the opposite sides and angles of a parallelogram are equal to one another ; also , its diameter bisects it ; for AB being equal to CD , and BC common , the two AB , BC are ...
Página 33
Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one an- other ; therefore the straight line AL is equal to BC .
Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one an- other ; therefore the straight line AL is equal to BC .
Página 61
In like manner it may be shewn that FD is greater than CD . Therefore DA is the greatest ; and DE greater than DF , and DF than DC . And because MK , KD are greater ( 13. 1. ) than MD , and MK is equal to MG , the remainder KD is ...
In like manner it may be shewn that FD is greater than CD . Therefore DA is the greatest ; and DE greater than DF , and DF than DC . And because MK , KD are greater ( 13. 1. ) than MD , and MK is equal to MG , the remainder KD is ...
Página 69
... the less than the greater , which is impossible ; wherefore FG is not perpendicular to DE : In the same manner it may be shewn , that no other line but FC can be perpendicular to DE ; FC is therefore perpendicular to DE .
... the less than the greater , which is impossible ; wherefore FG is not perpendicular to DE : In the same manner it may be shewn , that no other line but FC can be perpendicular to DE ; FC is therefore perpendicular to DE .
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Vista de fragmentos - 1836 |
Términos y frases comunes
ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circumference coincide common consequently construction cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremities fall fore four fourth given given straight line greater half Hence inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism Prob produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure remaining right angles segment shewn sides similar sine solid spherical square straight line taken tangent THEOR third touch 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 |
| Edición | 6 |
| Editor | W.E. Dean, 1836 |
| Largo | 311 páginas |
| Exportar cita | BiBTeX EndNote RefMan |