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 44
... ABCD is equal to the parallelogram EBCF . If the sides AD , DF of the paral- lelograms ABCD , DBCF opposite to the base BC be terminated in the same point D ; it is plain that each of the parallelograms is double ( 34 . 1. ) of the ...
... ABCD is equal to the parallelogram EBCF . If the sides AD , DF of the paral- lelograms ABCD , DBCF opposite to the base BC be terminated in the same point D ; it is plain that each of the parallelograms is double ( 34 . 1. ) of the ...
Página 45
... ABCD is equal to the parallelogram EBCF . Therefore , parallelograms upon the same base , & c . Q. E. D. PROP . XXXVI . THEOR . Parallelograms upon equal bases , and between the same parallels , are equal to one another . A DE H Let ABCD ...
... ABCD is equal to the parallelogram EBCF . Therefore , parallelograms upon the same base , & c . Q. E. D. PROP . XXXVI . THEOR . Parallelograms upon equal bases , and between the same parallels , are equal to one another . A DE H Let ABCD ...
Página 47
... ABCD and the triangle EBC be upon the same base BC and between the same pa- rallels BC , AE ; the parallelogram ABCD A is double of the triangle EBC . Join AC ; then the triangle ABC is equal ( 37. 1. ) to the triangle EBC , because ...
... ABCD and the triangle EBC be upon the same base BC and between the same pa- rallels BC , AE ; the parallelogram ABCD A is double of the triangle EBC . Join AC ; then the triangle ABC is equal ( 37. 1. ) to the triangle EBC , because ...
Página 48
... ABCD be a parallelogram of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is , through which AC passes , and let BK , KD be the other parallelograms , which make up the whole figure ABCD and are there- fore ...
... ABCD be a parallelogram of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is , through which AC passes , and let BK , KD be the other parallelograms , which make up the whole figure ABCD and are there- fore ...
Página 49
... ABCD be the given rectilineal figure , and E the given rectili- neal angle . It is required to describe a parallelogram equal to ABCD , and having an angle equal to E. G Join DB , and describe ( 42. 1. ) the OF GEOMETRY . BOOK . I. 49.
... ABCD be the given rectilineal figure , and E the given rectili- neal angle . It is required to describe a parallelogram equal to ABCD , and having an angle equal to E. G Join DB , and describe ( 42. 1. ) the OF GEOMETRY . BOOK . I. 49.
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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