The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 141
E B G multiples whaterer of the first and the third , and also any equimultiples whatever of the second and the fourth , then the multiple of the first shall have the same ratio to the multiple of the second , that the multiple of the ...
E B G multiples whaterer of the first and the third , and also any equimultiples whatever of the second and the fourth , then the multiple of the first shall have the same ratio to the multiple of the second , that the multiple of the ...
Página 153
THEOREM : Ratios that are the same to the same ratio , are the samo to one another , Let A be to B as C is to D , and let C be to D'as E is to F : A shall be to B as E is to F. G HK BD F L MN Take of A , C , E any equimultiples whatever ...
THEOREM : Ratios that are the same to the same ratio , are the samo to one another , Let A be to B as C is to D , and let C be to D'as E is to F : A shall be to B as E is to F. G HK BD F L MN Take of A , C , E any equimultiples whatever ...
Página 155
M G H A C E B DN KL For , because C has a greater ratio . to D than E has to F , there are some equimultiples of C and E , and some equimultiples of D and F , such that the multiple of C is greater than the multiple of D , but the ...
M G H A C E B DN KL For , because C has a greater ratio . to D than E has to F , there are some equimultiples of C and E , and some equimultiples of D and F , such that the multiple of C is greater than the multiple of D , but the ...
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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