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 9
AB to DE , and AC to DF ; and let the angle BAC be also equal to the angle EDF : then shall the base BC be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite ...
AB to DE , and AC to DF ; and let the angle BAC be also equal to the angle EDF : then shall the base BC be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite ...
Página 10
Whenever in two triangles these three things are equal , namely , BC = EF , B = E , and C = F , it may be inferred that the other three are equal also ; that is , AB = DE , AC = DF , and the angle BAC = DEF . PROP . III . THEOR .
Whenever in two triangles these three things are equal , namely , BC = EF , B = E , and C = F , it may be inferred that the other three are equal also ; that is , AB = DE , AC = DF , and the angle BAC = DEF . PROP . III . THEOR .
Página 11
... then shall the two triangles be identical , or have their angles equal , that is , those angles that are opposite to the equal sides ; namely , the angle BAC to the angle EDF , the angle ABC to DEF , and the angle ACB to DFE .
... then shall the two triangles be identical , or have their angles equal , that is , those angles that are opposite to the equal sides ; namely , the angle BAC to the angle EDF , the angle ABC to DEF , and the angle ACB to DFE .
Página 12
being equal to the angle BGA , and the angle CAG equal to the angle CGA , by equal additions , the sum of the two angles BAG , CAG , is equal to the sum of the two angles BGA , CGA , ( Ax . 2. ) that is , the whole an- gle BAC equal to ...
being equal to the angle BGA , and the angle CAG equal to the angle CGA , by equal additions , the sum of the two angles BAG , CAG , is equal to the sum of the two angles BGA , CGA , ( Ax . 2. ) that is , the whole an- gle BAC equal to ...
Página 14
rior angle ACD is greater than either of the interior opposite angles CBA , BAC . Join B and E the middle point of the line AC , and produce BE to F , and make EF equal to BE ; join also FC , and produce AC to G. B A E F D Because AE is ...
rior angle ACD is greater than either of the interior opposite angles CBA , BAC . Join B and E the middle point of the line AC , and produce BE to F , and make EF equal to BE ; join also FC , and produce AC to G. B A E F D Because AE is ...
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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 |