The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 135
a When four magnitudes are proportionals it is usually expressed by saying , the first is to the second as the third is to the fourth . 7. When of the equimultiples of four magnitudes , taken as in the fifth definition , the multiple of ...
a When four magnitudes are proportionals it is usually expressed by saying , the first is to the second as the third is to the fourth . 7. When of the equimultiples of four magnitudes , taken as in the fifth definition , the multiple of ...
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 240
B E F Let the two planes BA , BC be each of them perpendicular to a third plane , and let B D be the common section of the planes BA , BC : BD shall be perpendicular to the third plane . For , if not , from the point D , draw in the ...
B E F Let the two planes BA , BC be each of them perpendicular to a third plane , and let B D be the common section of the planes BA , BC : BD shall be perpendicular to the third plane . For , if not , from the point D , draw in 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