The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 137
Of this there are the two following kinds , which arise from the different order in which the magnitudes are taken , two and two . 19. Ex æquali . This term is used simply by itself , when the first magnitude is to the second of the ...
Of this there are the two following kinds , which arise from the different order in which the magnitudes are taken , two and two . 19. Ex æquali . This term is used simply by itself , when the first magnitude is to the second of the ...
Página 138
THEOREM , If any number of magnitudes be equimultiples of as many , each of each ; whatever multiple any one of them is of its part , the same multiple shall all the first magnitudes be of all the other . Let any number of magnitudes AB ...
THEOREM , If any number of magnitudes be equimultiples of as many , each of each ; whatever multiple any one of them is of its part , the same multiple shall all the first magnitudes be of all the other . Let any number of magnitudes AB ...
Página 148
Let A and B be equal magnitudes , and C any other magnitude : each of the magnitudes A and B shall have the same ratio to C ; and C shall have the same ratio to each of the magnitudes A and B. Take of A and B any equimultiples whatever ...
Let A and B be equal magnitudes , and C any other magnitude : each of the magnitudes A and B shall have the same ratio to C ; and C shall have the same ratio to each of the magnitudes A and B. Take of A and B any equimultiples whatever ...
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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