The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 103
B semicircle , shall be less than a right angle ; and the angle in the segment ADC , which is less than a semicircle , shall be greater than a right angle .. Join AE , and produce BAto F. Then , because EA is equal to EB ...
B semicircle , shall be less than a right angle ; and the angle in the segment ADC , which is less than a semicircle , shall be greater than a right angle .. Join AE , and produce BAto F. Then , because EA is equal to EB ...
Página 134
A LESS magnitude is said to be a part of a greater magnitude , when the less measures the greater ; that is , when the less is contained a certain number of times exactly in the greater . 2. A greatér magnitude is said to be a multiple ...
A LESS magnitude is said to be a part of a greater magnitude , when the less measures the greater ; that is , when the less is contained a certain number of times exactly in the greater . 2. A greatér magnitude is said to be a multiple ...
Página 153
But it has been shewn that if G be greater than L , H is greater than M ; and if equal , equal ; and if less , less . Therefore if G be greater than L , K is greater than N ; and if equal , equal ; and if less , less .
But it has been shewn that if G be greater than L , H is greater than M ; and if equal , equal ; and if less , less . Therefore if G be greater than L , K is greater than N ; and if equal , equal ; and if less , less .
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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