The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 53
B If there be two straight lines , one of which is divided into any number of parts , the rectangle contained by the trov straight lines is equal to the rectangles contained by the undicided line , and the several parts of the divided ...
B If there be two straight lines , one of which is divided into any number of parts , the rectangle contained by the trov straight lines is equal to the rectangles contained by the undicided line , and the several parts of the divided ...
Página 188
Let AB be the straight line given to be divided , and AC the given divided straight line : it is required to divide AB similarly to AC . Let AC be divided at the points D , E , and let AB , AC be placed so as to contain any angle ...
Let AB be the straight line given to be divided , and AC the given divided straight line : it is required to divide AB similarly to AC . Let AC be divided at the points D , E , and let AB , AC be placed so as to contain any angle ...
Página 285
9 is a particular case ) of VI . io The most important case of this proposition is that in which a straight line is to be divided either internally or ex ternally into two parts which shall be in a given ratio .
9 is a particular case ) of VI . io The most important case of this proposition is that in which a straight line is to be divided either internally or ex ternally into two parts which shall be in a given ratio .
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ABCD angle ABC angle ACB angle BAC Axiom base BC is equal bisected Book centre circle circle ABC circumference common Construction contained Corollary Definition demonstration described diameter divided double draw drawn edition Elements equal equal angles equiangular equilateral equimultiples Euclid exterior angle extremities fall figure four fourth given straight line greater half Hypothesis impossible join less Let ABC magnitudes manner meet multiple namely parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals Q.E.D. PROPOSITION ratio reason rectangle rectangle contained rectilineal figure right angles segment shewn sides similar Simson solid square straight line &c suppose Take taken THEOREM third touches the circle triangle ABC Wherefore whole