The Elements of EuclidJohnson and Warner, 1811 - 518 páginas |
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Página 319
... given a more explicit demonstration than that which is now in the Elements . PROP . X. B. V. It was necessary to give another demonstr tion of this pro- position , because that which is in the Greek and Latin , or other editions , is ...
... given a more explicit demonstration than that which is now in the Elements . PROP . X. B. V. It was necessary to give another demonstr tion of this pro- position , because that which is in the Greek and Latin , or other editions , is ...
Página 324
... given a good demonstration of it which we have put in pro- position E ; but he makes it a corollary from the 19th , and be- gins it with the words , " Hence it easily follows , " though it does not at all follow from it . PROP . XX ...
... given a good demonstration of it which we have put in pro- position E ; but he makes it a corollary from the 19th , and be- gins it with the words , " Hence it easily follows , " though it does not at all follow from it . PROP . XX ...
Página 341
... position of the sides which contain the figures , to one another , depending partly upon each of these : and , for ... given no definition of equal figures , and it is certain he did not give this : for what is Book XI . Book XI . called ...
... position of the sides which contain the figures , to one another , depending partly upon each of these : and , for ... given no definition of equal figures , and it is certain he did not give this : for what is Book XI . Book XI . called ...
Página 351
... given ; but he does not demonstrate the second and third cases : the ... position , because the planes containing the solids which are to be ... mentioned in this proposition are si ilar , that the equality of the solids in prop 25 , may ...
... given ; but he does not demonstrate the second and third cases : the ... position , because the planes containing the solids which are to be ... mentioned in this proposition are si ilar , that the equality of the solids in prop 25 , may ...
Página 367
... given , and the ratios of their sides given . IV . Points , lines , and spaces are said to be given in position , which have always the same situation , and which are either actual- ly exhibited , or can be found . A. An angle is said to be ...
... given , and the ratios of their sides given . IV . Points , lines , and spaces are said to be given in position , which have always the same situation , and which are either actual- ly exhibited , or can be found . A. An angle is said to be ...
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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