The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 148
... ratio to C ; and C shall have the same ratio to each of the magnitudes A and B. Take of A and B any equimultiples ... greater than F , E is greater than F ; and if equal , equal ; and if less , less . But D and E are any ...
... ratio to C ; and C shall have the same ratio to each of the magnitudes A and B. Take of A and B any equimultiples ... greater than F , E is greater than F ; and if equal , equal ; and if less , less . But D and E are any ...
Página 155
... greater ratio than the fifth has to the sixth . Let A the first have the same ratio to B the second that C the third has to D the fourth , but C the third a greater ratio to D the fourth than E the fifth to F the sixth : A the first ...
... greater ratio than the fifth has to the sixth . Let A the first have the same ratio to B the second that C the third has to D the fourth , but C the third a greater ratio to D the fourth than E the fifth to F the sixth : A the first ...
Página 156
... ratio to the fourth that the fifth has to the sixth , it may be shewn , in the same manner , that the first has a greater ratio to the second than the fifth has to the sixth . PROPOSITION 14. THEOREM . If the first have the same ...
... ratio to the fourth that the fifth has to the sixth , it may be shewn , in the same manner , that the first has a greater ratio to the second than the fifth has to the sixth . PROPOSITION 14. THEOREM . If the first have the same ...
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Términos y frases comunes
ABCD 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 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 whole angle