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 10
occurring at the same time in the two straight lines ED and FD , must fall on their intersection D ; consequently , the two triangles BAC , EDF , are identical , or mutually equal ( Ax . 8. ) . COROLLARY . Whenever in two triangles ...
occurring at the same time in the two straight lines ED and FD , must fall on their intersection D ; consequently , the two triangles BAC , EDF , are identical , or mutually equal ( Ax . 8. ) . COROLLARY . Whenever in two triangles ...
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these two angles are together equal to two right angles ; and the angle ADC is acute , because the angle ABD is right ; consequently , the angle ACD is greater than the angle ADC ; and , since the greater side is opposite to the greater ...
these two angles are together equal to two right angles ; and the angle ADC is acute , because the angle ABD is right ; consequently , the angle ACD is greater than the angle ADC ; and , since the greater side is opposite to the greater ...
Página 19
and consequently AH = DF . Now ( by hyp . ) , we have DF = AC ; and therefore , AH = AC . But by the last proposition , the ob- lique line AC cannot be equal to the oblique line AH , which lies A nearer to the perpendicular AB ...
and consequently AH = DF . Now ( by hyp . ) , we have DF = AC ; and therefore , AH = AC . But by the last proposition , the ob- lique line AC cannot be equal to the oblique line AH , which lies A nearer to the perpendicular AB ...
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... there consequently re- mains the angle BAC = EDF . COR . If BA , AC be produced to I and H , the angle BAC = HAI ; hence , the angle HAI is also equal to EDF . SCHOLIUM . I A H D F The restriction of this proposition to the case ...
... there consequently re- mains the angle BAC = EDF . COR . If BA , AC be produced to I and H , the angle BAC = HAI ; hence , the angle HAI is also equal to EDF . SCHOLIUM . I A H D F The restriction of this proposition to the case ...
Página 25
or have their corresponding angles equal ; consequently , the op- posite sides are parallel ; namely , the side AB parallel to CD , and BD pa- rallel to AC ; and , therefore , the figure is a parallelogram . COR . 3.
or have their corresponding angles equal ; consequently , the op- posite sides are parallel ; namely , the side AB parallel to CD , and BD pa- rallel to AC ; and , therefore , the figure is a parallelogram . COR . 3.
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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 |