The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 23
... greater than AB . Wherefore , the greater angle & c . Q.E.D. 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 greater than the ...
... greater than AB . Wherefore , the greater angle & c . Q.E.D. 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 greater than the ...
Página 151
... 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 equimultiples of A and B , and F the multiple of C ; so that D is greater than F , but E ...
... 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 equimultiples of A and B , and F the multiple of C ; so that D is greater than F , but E ...
Página 155
... greater ratio than E the fifth has to F the sixth . H- M- A- C- E- B D F N L K- For , because C has a greater ratio to D than E has to F , there are some equimultiples of C and E , and some equi- multiples of D and F , such that the ...
... greater ratio than E the fifth has to F the sixth . H- M- A- C- E- B D F N L K- For , because C has a greater ratio to D than E has to F , there are some equimultiples of C and E , and some equi- multiples of D and F , such that the ...
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ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC 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