The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 203
But any rectilineal figure described on AB is to the similar and similarly described rectilineal figure on FG in the duplicate ratio of AB to FG , ( Corollary 1 . Therefore as AB is to M , so is the figure on AB to the figure on FG ...
But any rectilineal figure described on AB is to the similar and similarly described rectilineal figure on FG in the duplicate ratio of AB to FG , ( Corollary 1 . Therefore as AB is to M , so is the figure on AB to the figure on FG ...
Página 204
I four straight lines be proportionals , the similar rectilineal figures similarly described on them shall also be ... NH be similarly described : the figure KAB shall be to the figure LCD as the figuro MĚ is to the figure NH .
I four straight lines be proportionals , the similar rectilineal figures similarly described on them shall also be ... NH be similarly described : the figure KAB shall be to the figure LCD as the figuro MĚ is to the figure NH .
Página 209
13 . and on GH describe the rectilineal figure KGH , similar and similarly situated to the rectilineal figure ABC [ VI , 18 . KGH shall be the rectilineal figure required . For , because BC is to GH as GH is to CF , [ Construction . and ...
13 . and on GH describe the rectilineal figure KGH , similar and similarly situated to the rectilineal figure ABC [ VI , 18 . KGH shall be the rectilineal figure required . For , because BC is to GH as GH is to CF , [ Construction . and ...
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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