The Elements of Euclid, Libros 1-6;Libro 11 |
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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 140
I Let A the first be the same multiple of B the second , that C the third is of D the fourth ; and of A and C let the equimultiples EF and GH be taken : EF shall be the same multiple of B that GH is of D. For , because EF is the same ...
I Let A the first be the same multiple of B the second , that C the third is of D the fourth ; and of A and C let the equimultiples EF and GH be taken : EF shall be the same multiple of B that GH is of D. For , because EF is the same ...
Página 151
B some equimultiples of A and B , ånd some multiple of C , such that the multiple of A is greater than the multiple of C , but the multiple of B is not greater than the multiple of C. Let such multiples be taken ; and let D and E be the ...
B some equimultiples of A and B , ånd some multiple of C , such that the multiple of A is greater than the multiple of C , but the multiple of B is not greater than the multiple of C. Let such multiples be taken ; and let D and E be 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