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, Edlemnts of Plane and Spherical Trigonometry |
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Página 45
DK = BG = A . In like manner , EH-A.EC . Therefore A.BC = A : BD + A.DE + A.EC ; that is , the rectangle A.BC is equal to the several rectangles A.BD , A.DE , A.EC. SCHOLIUM . The properties of the sections of lines , demonstrated in ...
DK = BG = A . In like manner , EH-A.EC . Therefore A.BC = A : BD + A.DE + A.EC ; that is , the rectangle A.BC is equal to the several rectangles A.BD , A.DE , A.EC. SCHOLIUM . The properties of the sections of lines , demonstrated in ...
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 .
Página 70
... which is impossible ; Wherefore F is not the centre of the circle ABC : In the same manner it may be shewn , that no other point which is not in CA , is the centre ; that is , the centre is in CA. B D F E PROP . XX . THEOR .
... which is impossible ; Wherefore F is not the centre of the circle ABC : In the same manner it may be shewn , that no other point which is not in CA , is the centre ; that is , the centre is in CA. B D F E PROP . XX . THEOR .
Página 71
... the same manner , the angles BAD , DCB may be shewn to be equal to two right angles . COR . 1. If any side of a quadrilateral be OF GEOMETRY . BOOK III . 71.
... the same manner , the angles BAD , DCB may be shewn to be equal to two right angles . COR . 1. If any side of a quadrilateral be OF GEOMETRY . BOOK III . 71.
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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 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, Edlemnts of Plane and Spherical Trigonometry |
| Autor | John Playfair |
| Edición | 6 |
| Editor | W.E. Dean, 1836 |
| Largo | 311 páginas |
| Exportar cita | BiBTeX EndNote RefMan |