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 44
So likewise the square de- scribed on the double of a line is evidently four times the square described on a single one ; on a triple line nine times that on a single one , & c . 3. In every parallelogram , any of the parallelograms ...
So likewise the square de- scribed on the double of a line is evidently four times the square described on a single one ; on a triple line nine times that on a single one , & c . 3. In every parallelogram , any of the parallelograms ...
Página 50
... we shall have , 4ab + c2 = c2 + 4bc + 462 , or 4ab + c2 ( c + 26 ) 2 . PROP . IX . THEOR . If a straight line be divided into two equal , and also into two unequal parts ; the squares of the two unequal parts are together double ...
... we shall have , 4ab + c2 = c2 + 4bc + 462 , or 4ab + c2 ( c + 26 ) 2 . PROP . IX . THEOR . If a straight line be divided into two equal , and also into two unequal parts ; the squares of the two unequal parts are together double ...
Página 51
... of half the line bisected , and of the square of the line made up of the half and the part produced . Let the straight line AB be bisected in C , and produced to the point D ; the squares of AD , DB are double of the squares of AC ...
... of half the line bisected , and of the square of the line made up of the half and the part produced . Let the straight line AB be bisected in C , and produced to the point D ; the squares of AD , DB are double of the squares of AC ...
Página 53
... triangle be bisected , the sum of the squares of the other two sides is double of the square of half the side bisected , and of the square of the line drawn from the point of bisection to the opposite angle of the triangle .
... triangle be bisected , the sum of the squares of the other two sides is double of the square of half the side bisected , and of the square of the line drawn from the point of bisection to the opposite angle of the triangle .
Página 66
For the same reason , CD is double of CG : But AB is equal to CD ; there- fore AF is equal to CG : And because AE is equal to EC , the square of AE is equal to the square of EC : Now the squares of AF , FE are equal ( 37.
For the same reason , CD is double of CG : But AB is equal to CD ; there- fore AF is equal to CG : And because AE is equal to EC , the square of AE is equal to the square of EC : Now the squares of AF , FE are equal ( 37.
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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 |