The Elements of EuclidJohnson and Warner, 1811 - 518 páginas |
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Página 21
... sides BA , CA do not coincide with the sides ED , FD , but have a different situation , as EG , FG ; then , upon the same base EF , and upon the same side of it , there can be two triangles that have their sides which are terminated in ...
... sides BA , CA do not coincide with the sides ED , FD , but have a different situation , as EG , FG ; then , upon the same base EF , and upon the same side of it , there can be two triangles that have their sides which are terminated in ...
Página 26
... side of a triangle be produced , the exterior angle is greater than either of the interior ... sides are op- posite ; wherefore the angle BAE is equal to the angle ECF ... B A + these add the angle ACB ; therefore the angles 26 THE ELEMENTS.
... side of a triangle be produced , the exterior angle is greater than either of the interior ... sides are op- posite ; wherefore the angle BAE is equal to the angle ECF ... B A + these add the angle ACB ; therefore the angles 26 THE ELEMENTS.
Página 27
... side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle ABC , is also ... B A a 5. 1 . Съ 18. 1 Book I , but it is not ; therefore the OF EUCLID . 2.7.
... side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle ABC , is also ... B A a 5. 1 . Съ 18. 1 Book I , but it is not ; therefore the OF EUCLID . 2.7.
Página 28
... sides of a triangle are together greater than the third side . Let ABC be a triangle ' ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and ...
... sides of a triangle are together greater than the third side . Let ABC be a triangle ' ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and ...
Página 29
... sides BA , AC are greater than BE , EC : again , because the two sides CE , ED of the triangle CED are great- er than CD , add DB to each of these ; therefore the sides CE , EB are greater than CD , DB ; but it has been shown that BA ...
... sides BA , AC are greater than BE , EC : again , because the two sides CE , ED of the triangle CED are great- er than CD , add DB to each of these ; therefore the sides CE , EB are greater than CD , DB ; but it has been shown that BA ...
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Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore