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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
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Página 30
... angle DBA is equal to the two angles DBE , EBA ; add to each of these equals the angle ABC ; then will the two angles DBA , ABC be equal to the three angles DBE , EBA , ABC ; but the angles CBE , EBD have been demonstrated to be equal ...
... angle DBA is equal to the two angles DBE , EBA ; add to each of these equals the angle ABC ; then will the two angles DBA , ABC be equal to the three angles DBE , EBA , ABC ; but the angles CBE , EBD have been demonstrated to be equal ...
Página 32
... angle ACD , is greater than the angle ABC . Therefore if one side , & c . Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles together are ...
... angle ACD , is greater than the angle ABC . Therefore if one side , & c . Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles together are ...
Página 33
... ABC be a triangle , of which the angle ABC is greater than the angle BCA ; the side AC is likewise greater than the side AB . For , if it be not greater , AC must either be equal to AB , or less than it ; it is not equal , because then ...
... ABC be a triangle , of which the angle ABC is greater than the angle BCA ; the side AC is likewise greater than the side AB . For , if it be not greater , AC must either be equal to AB , or less than it ; it is not equal , because then ...
Página 34
... triangle ABC , to the point D within it ; BD and DC are less than the other two sides BA , AC of the triangle , but contain an angle BDC greater than the angle BAC . Produce BD to E ; and because two sides of a triangle ( 20. 1. ) are ...
... triangle ABC , to the point D within it ; BD and DC are less than the other two sides BA , AC of the triangle , but contain an angle BDC greater than the angle BAC . Produce BD to E ; and because two sides of a triangle ( 20. 1. ) are ...
Página 36
... angle contained by the two sides of the other ; the base of that which has the greater angle shall be greater than the base of the other . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two DE , DF each to ...
... angle contained by the two sides of the other ; the base of that which has the greater angle shall be greater than the base of the other . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two DE , DF each to ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore