The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 53
... divided into any number of parts , the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line , and the several parts of the divided line . Let A and BC be two straight lines ; and let ...
... divided into any number of parts , the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line , and the several parts of the divided line . Let A and BC be two straight lines ; and let ...
Página 188
... divided straight line have . 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 ...
... divided straight line have . 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 ...
Página 285
... divided internally is given in the text ; suppose , for example , that the given ratio is that of AE to EC ; then AB is divided at G in the given ratio . Suppose , however , that AB is to be divided externally in a given ratio ; that is ...
... divided internally is given in the text ; suppose , for example , that the given ratio is that of AE to EC ; then AB is divided at G in the given ratio . Suppose , however , that AB is to be divided externally in a given ratio ; that is ...
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ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC bisected centre circle ABC circumference Constr Construction Corollary Definition 15 demonstration diameter double draw equal angles equal to F equiangular equimultiples Euclid Euclid's Elements exterior angle fourth given circle given straight line gnomon greater ratio greater than F Hypothesis less Let ABC Let the straight meet multiple opposite angle parallel to BC parallelogram perpendicular polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION rectangle contained remaining angle right angles segment shewn sides similar and similarly Simson square described square on AC straight line &c straight line AB THEOREM tiples touches the circle triangle ABC triangle DEF twice the rectangle Wherefore