The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 136
... proportionals , so that they continue still to be proportionals . 13. Permutando , or alternando , by permutation or alternately ; when there are four proportionals , and it is inferred that the first is to the third , as the second is ...
... proportionals , so that they continue still to be proportionals . 13. Permutando , or alternando , by permutation or alternately ; when there are four proportionals , and it is inferred that the first is to the third , as the second is ...
Página 158
... proportionals , they shall also be proportionals when taken alternately . Let A , B , C , D be four magnitudes of the same kind which are proportionals ; namely , as A is to B so let a be to D : they shall also be proportionals when ...
... proportionals , they shall also be proportionals when taken alternately . Let A , B , C , D be four magnitudes of the same kind which are proportionals ; namely , as A is to B so let a be to D : they shall also be proportionals when ...
Página 204
... proportionals , the similar rec- tilineal figures similarly described on them shall also be proportionals ; and if the similar rectilineal figures simi- larly described on four straight lines be proportionals , those straight lines ...
... proportionals , the similar rec- tilineal figures similarly described on them shall also be proportionals ; and if the similar rectilineal figures simi- larly described on four straight lines be proportionals , those straight lines ...
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Términos y frases comunes
ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC bisected centre circle ABC circumference Constr Construction Corollary Definition 15 demonstration diameter double draw equal angles equal to F equiangular equimultiples Euclid Euclid's Elements exterior angle fourth given circle given straight line gnomon greater ratio greater than F Hypothesis less Let ABC Let the straight meet multiple opposite angle parallel to BC parallelogram perpendicular polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION rectangle contained remaining angle right angles segment shewn sides similar and similarly Simson square described square on AC straight line &c straight line AB THEOREM tiples touches the circle triangle ABC triangle DEF twice the rectangle Wherefore