The Elements of Euclid, Libros 1-6;Libro 11 |
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Página xvii
The propositions are of two kinds , problems and theorems . In a problem something is required to be done ; in a theorem some new principle is asserted to be true . A proposition consists of various parts . We have first the general ...
The propositions are of two kinds , problems and theorems . In a problem something is required to be done ; in a theorem some new principle is asserted to be true . A proposition consists of various parts . We have first the general ...
Página 171
THEOREM . If the first have to the second the same ratio which the third has to the fourth , and the fifth have to the second the same ratio which the sixth has to the fourth , then the first and fifth together shall have to the second ...
THEOREM . If the first have to the second the same ratio which the third has to the fourth , and the fifth have to the second the same ratio which the sixth has to the fourth , then the first and fifth together shall have to the second ...
Página 217
PROPOSITION B. THEOREM . If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base , the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the ...
PROPOSITION B. THEOREM . If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base , the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the ...
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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