Elements of Geometry; Containing the First Six Books of Euclid ...For Bell & Bradfute, 1814 - 461 Seiten |
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Seite 52
... ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC ; the parallelogram ABCD is equal to the parallelogram EBCF . If the sides AD , DF of the parallelograms ABCD , DBCF opposite to the base BC be terminated in ...
... ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC ; the parallelogram ABCD is equal to the parallelogram EBCF . If the sides AD , DF of the parallelograms ABCD , DBCF opposite to the base BC be terminated in ...
Seite 53
... ABCD f3 . Ax . is equal to the parallelogram EBCF . Therefore , paral- lelograms 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 . Let ...
... ABCD f3 . Ax . is equal to the parallelogram EBCF . Therefore , paral- lelograms 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 . Let ...
Seite 54
... ABCD , because it is upon the same base BC , and between the same parallels BC , AH : For the like reason , the parallelogram EFGH is equal to the same EBCH : Therefore also the parallelogram ABCD is equal to EFGH . Wherefore ...
... ABCD , because it is upon the same base BC , and between the same parallels BC , AH : For the like reason , the parallelogram EFGH is equal to the same EBCH : Therefore also the parallelogram ABCD is equal to EFGH . Wherefore ...
Seite 56
... ABCD and the triangle EBC upon the same base BC , and between the same parallels BC , AE ; the parallelogram ABCD is double of the triangle EBC . Join AC ; then the triangle ABC is equal a to the triangle EBC , because they are upon the ...
... ABCD and the triangle EBC upon the same base BC , and between the same parallels BC , AE ; the parallelogram ABCD is double of the triangle EBC . Join AC ; then the triangle ABC is equal a to the triangle EBC , because they are upon the ...
Seite 57
... ABCD is also double of the triangle EBC . Therefore , if a parallelo- gram , & c . Q. E. D. PROP . XLII . PROB . To describe a parallelogram that shall be equal to a given triangle , and have one of its angles equal to a given ...
... ABCD is also double of the triangle EBC . Therefore , if a parallelo- gram , & c . Q. E. D. PROP . XLII . PROB . To describe a parallelogram that shall be equal to a given triangle , and have one of its angles equal to a given ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch AC base BC bisected Book centre circle ABC circumference cosine cylinder definition demonstrated described diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles GEOMETRY given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram perpendicular polygon prism PROB proportional 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 SPHERICAL TRIGONOMETRY straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore