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 86
Any regular polygon may be inscribed in a circle , and circumscribed about one . Let ABCDE , & c . be a regular polygon : describe a circle through the three points A , B , C , the centre being O , and OP the perpendicular let fall from ...
Any regular polygon may be inscribed in a circle , and circumscribed about one . Let ABCDE , & c . be a regular polygon : describe a circle through the three points A , B , C , the centre being O , and OP the perpendicular let fall from ...
Página 87
The point O , the common centre of the inscribed and circumscribed circles , may also be regarded as the centre of the polygon ... To inscribe a regular polygon of a certain number of sides in a given circle , we have only to divide the ...
The point O , the common centre of the inscribed and circumscribed circles , may also be regarded as the centre of the polygon ... To inscribe a regular polygon of a certain number of sides in a given circle , we have only to divide the ...
Página 88
to the remaining angle EDF : Wherefore the triangle ABC is equiangular to the triangle DEF , and it is inscribed in the circle ABC . PROP . III . PROB . About a given circle to describe a triangle equiangular to a given triangle .
to the remaining angle EDF : Wherefore the triangle ABC is equiangular to the triangle DEF , and it is inscribed in the circle ABC . PROP . III . PROB . About a given circle to describe a triangle equiangular to a given triangle .
Página 89
Let the given triangle be ABC ; it is required to inscribe a circle in ABC . ... Therefore the straight lines AB , BC , CA , do each of them touch the circle , and the cir- cle EFG is inscribed in the triangle ABC . SCHOLIUM .
Let the given triangle be ABC ; it is required to inscribe a circle in ABC . ... Therefore the straight lines AB , BC , CA , do each of them touch the circle , and the cir- cle EFG is inscribed in the triangle ABC . SCHOLIUM .
Página 90
AD : AE :: √2 : 1 ; hence the side of the inscribed square is to the radius , as the square root of 2 , is to unity . PROP . VI . PROB . To describe a square about a given circle . Let ABCD be the given circle ; it is required to ...
AD : AE :: √2 : 1 ; hence the side of the inscribed square is to the radius , as the square root of 2 , is to unity . PROP . VI . PROB . To describe a square about a given circle . Let ABCD be the given circle ; it is required to ...
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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 |