The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 23
Therefore AC is greater than AB . Wherefore , the greater angle & c . Q.E.D. a PROPOSITION 20. THEOREM . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle : any two sides of it are together ...
Therefore AC is greater than AB . Wherefore , the greater angle & c . Q.E.D. a PROPOSITION 20. THEOREM . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle : any two sides of it are together ...
Página 151
B some equimultiples of A and B , ånd some multiple of C , such that the multiple of A is greater than the multiple of C , but the multiple of B is not greater than the multiple of C. Let such multiples be taken ; and let D and E be the ...
B some equimultiples of A and B , ånd some multiple of C , such that the multiple of A is greater than the multiple of C , but the multiple of B is not greater than the multiple of C. Let such multiples be taken ; and let D and E be the ...
Página 155
ratio than the fifth to the sixth , the first shall have to the second a 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 the third a greater ...
ratio than the fifth to the sixth , the first shall have to the second a 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 the third a greater ...
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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