The Elements of EuclidJohnson and Warner, 1811 - 518 páginas |
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Página 21
... bisected by which was to be done . PROP . X. PROB . TO bisect a given finite straight line , that is , to di- vide it into two equal parts . Let AB be the given straight line : it is required to divide it into two equal parts . Describe ...
... bisected by which was to be done . PROP . X. PROB . TO bisect a given finite straight line , that is , to di- vide it into two equal parts . Let AB be the given straight line : it is required to divide it into two equal parts . Describe ...
Página 26
... Bisect AC in E , join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because ... bisected , it may be demonstrated that the angle d 15. 1 . BCG , that is , the angle ACD , is greater than the angle ...
... Bisect AC in E , join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because ... bisected , it may be demonstrated that the angle d 15. 1 . BCG , that is , the angle ACD , is greater than the angle ...
Página 44
... Bisect a BC in E , join AE , and at the point E in the straight line EC make the angle CEF equal to D ; and through A draw AG parallel to EC , and through C draw CG parallel to EF : therefore FECG is a parallelo- gram : and because BE ...
... Bisect a BC in E , join AE , and at the point E in the straight line EC make the angle CEF equal to D ; and through A draw AG parallel to EC , and through C draw CG parallel to EF : therefore FECG is a parallelo- gram : and because BE ...
Página 56
... bisected , and produced to any point ; the rectangle contained by the whole line thus produced , and the part of it produced , together withi the square of half the line bisected , is equal to the square of the straight line which is ...
... bisected , and produced to any point ; the rectangle contained by the whole line thus produced , and the part of it produced , together withi the square of half the line bisected , is equal to the square of the straight line which is ...
Página 60
... bisected , and of the square of the line made up of the half and the part produced . Let the straight line AB be bisected in C , and produced to the point D ; the squares of AD , DB are double of the squares of AC , CD . From the point ...
... bisected , and of the square of the line made up of the half and the part produced . Let the straight line AB be bisected in C , and produced to the point D ; the squares of AD , DB are double of the squares of AC , CD . From the point ...
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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