The Elements of EuclidJohnson and Warner, 1811 - 518 páginas |
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Página 11
... polygons , by more than four straight lines . XXIV . Of three sided figures , an equilateral triangle is that which has three equal sides . XXV . An isosceles triangle , is that which has only two sides equal . Book L A A A XXVI . A ...
... polygons , by more than four straight lines . XXIV . Of three sided figures , an equilateral triangle is that which has three equal sides . XXV . An isosceles triangle , is that which has only two sides equal . Book L A A A XXVI . A ...
Página 176
... polygon ABCDE has to the polygon FGHKL the duplicate ratio of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the polygon ABCDE is · similar to the polygon FGHKL , the angle BAE 176 THE ELEMENTS.
... polygon ABCDE has to the polygon FGHKL the duplicate ratio of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the polygon ABCDE is · similar to the polygon FGHKL , the angle BAE 176 THE ELEMENTS.
Página 177
... polygons have to one another , the antecedents being ABE , EBC , ECD , and the consequents FGL , LGH , LHK : and the polygon ABCDE has to the polygon FGHKL the duplicate ratio of that which the side AB has to the homologous side FG ...
... polygons have to one another , the antecedents being ABE , EBC , ECD , and the consequents FGL , LGH , LHK : and the polygon ABCDE has to the polygon FGHKL the duplicate ratio of that which the side AB has to the homologous side FG ...
Página 178
... polygon ABCDE to the polygon FGHKL ; but the triangle ABE has to the triangle FGL , the duplicate ratio of that which the side AB has to the homolo gous side FG . Therefore also the polygon ABCDE has to the polygon FGHKL the duplicate ...
... polygon ABCDE to the polygon FGHKL ; but the triangle ABE has to the triangle FGL , the duplicate ratio of that which the side AB has to the homolo gous side FG . Therefore also the polygon ABCDE has to the polygon FGHKL the duplicate ...
Página 214
... polygon BCDEF : there- B A C D fore all the angles at the bases of the triangle are together greater than all the angles of the polygon : and THE ELEMENTS.
... polygon BCDEF : there- B A C D fore all the angles at the bases of the triangle are together greater than all the angles of the polygon : and THE ELEMENTS.
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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