The Elements of EuclidJ. M. Dent & sons, 1933 - 298 páginas |
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Página 153
... equimultiples whatever G , H , K ; and of B , D , F any equimultiples whatever L , M , Ñ . Then , because A is to B as C is to D , [ Hypothesis . and that G and H are equimultiples of A and C , and L and M are equimultiples of B and D ...
... equimultiples whatever G , H , K ; and of B , D , F any equimultiples whatever L , M , Ñ . Then , because A is to B as C is to D , [ Hypothesis . and that G and H are equimultiples of A and C , and L and M are equimultiples of B and D ...
Página 155
... equimultiples of C and E , and some equi- multiples of D and F , such that the multiple of C is greater than the multiple of D , but the multiple of E is not greater than the multiple of F. [ V. Definition 7 . Let such multiples be ...
... equimultiples of C and E , and some equi- multiples of D and F , such that the multiple of C is greater than the multiple of D , but the multiple of E is not greater than the multiple of F. [ V. Definition 7 . Let such multiples be ...
Página 158
... equimultiples whatever E and F , and of C and D any equimultiples whatever G and H. Then , because E is the same multiple of A that F is of B , and that magnitudes have the same ratio to one another that their equimultiples have ...
... equimultiples whatever E and F , and of C and D any equimultiples whatever G and H. Then , because E is the same multiple of A that F is of B , and that magnitudes have the same ratio to one another that their equimultiples have ...
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Términos y frases comunes
ABCD adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC BC is equal bisected centre circle ABC circumference Constr Construction 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