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 16
is greater than the interior and opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that ...
is greater than the interior and opposite angle , the exterior angle BDC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ; and it has been demonstrated that ...
Página 22
... for the same reason , GAC is equal to GDE ; there consequently remains the angle BAC = EDF . D Cor . If BA , AC be produced to I and H , the angle BAC = HAI ; hence , the angle HAI is also equal to EDF . SCHOLIUM .
... for the same reason , GAC is equal to GDE ; there consequently remains the angle BAC = EDF . D Cor . If BA , AC be produced to I and H , the angle BAC = HAI ; hence , the angle HAI is also equal to EDF . SCHOLIUM .
Página 26
But , if the sides AD , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ; then , because ABCD is a parallelogram , AD is equal ( 28. 1. ) to BC ; for the same reason EF is equal to BC ...
But , if the sides AD , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ; then , because ABCD is a parallelogram , AD is equal ( 28. 1. ) to BC ; for the same reason EF is equal to BC ...
Página 27
1 ) to ABCD , because it is upon the same base BC , and between the same parallels BC , AH ; For the like reason , the parallelogram EFGH is equal to the same EBCH : Therefore also the parallelogram ABCD is equal to EFGH . PROP . XXXI .
1 ) to ABCD , because it is upon the same base BC , and between the same parallels BC , AH ; For the like reason , the parallelogram EFGH is equal to the same EBCH : Therefore also the parallelogram ABCD is equal to EFGH . PROP . XXXI .
Página 30
to the triangle ADC ; And because EKHA is a parallelogram , and AK its diameter , the triangle AEK B G C is equal to the triangle AHK For the same reason , the triangle KGC is equal to the triangle KFC . Then , because the triangle AEK ...
to the triangle ADC ; And because EKHA is a parallelogram , and AK its diameter , the triangle AEK B G C is equal to the triangle AHK For the same reason , the triangle KGC is equal to the triangle KFC . Then , because the triangle AEK ...
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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 distance 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 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 |
| Editor | W. E. Dean, 1836 |
| Largo | 311 páginas |
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