The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 41
Then each of the figures EBCA , DBCF is a parallelogram ; [ Definition . and EBCA is equal to DBCF , because they are on the same base BC , and between the same parallels BC , EF . [ I. 35 . And the triangle ABC is half of the ...
Then each of the figures EBCA , DBCF is a parallelogram ; [ Definition . and EBCA is equal to DBCF , because they are on the same base BC , and between the same parallels BC , EF . [ I. 35 . And the triangle ABC is half of the ...
Página 63
And because AC is equal to CE , [ Construction . the square on AC is equal to the square on CE ; therefore the squares on AC , CE are double of the square on AC . But the square on AE is equal to the squares on AC , CE , because the ...
And because AC is equal to CE , [ Construction . the square on AC is equal to the square on CE ; therefore the squares on AC , CE are double of the square on AC . But the square on AE is equal to the squares on AC , CE , because the ...
Página 201
But , because the polygons are similar , [ Hypothesis . therefore the whole angle ABC is equal to the whole angle FGH ; ( VI . Definition 1 . therefore the remaining angle EBC is equal to the remaining angle LGH . [ Axiom 3 .
But , because the polygons are similar , [ Hypothesis . therefore the whole angle ABC is equal to the whole angle FGH ; ( VI . Definition 1 . therefore the remaining angle EBC is equal to the remaining angle LGH . [ Axiom 3 .
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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