The Elements of EuclidJ. M. Dent & sons, 1933 - 298 páginas |
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Página xi
... axioms ( or " common notions " as he called them ) , but as postulates , Thus " Axiom 11 , " that all right angles are equal to one another , was Euclid's " Postulate 4 , " while " Axiom 12 " ( the well - known parallel - axiom ) was ...
... axioms ( or " common notions " as he called them ) , but as postulates , Thus " Axiom 11 , " that all right angles are equal to one another , was Euclid's " Postulate 4 , " while " Axiom 12 " ( the well - known parallel - axiom ) was ...
Página 253
... axiom as this is required , for example , in I. 17. A similar remark applies to the fifth axiom . In the eighth axiom the words " that is , which exactly fill the same space , " have been introduced without the authority of the original ...
... axiom as this is required , for example , in I. 17. A similar remark applies to the fifth axiom . In the eighth axiom the words " that is , which exactly fill the same space , " have been introduced without the authority of the original ...
Página 263
... axiom as difficult as his , and then an intricate series of proposi- tions ; while in Euclid's method after the axiom is once admitted the remaining process is simple and clear . One modification of Euclid's axiom has been proposed ...
... axiom as difficult as his , and then an intricate series of proposi- tions ; while in Euclid's method after the axiom is once admitted the remaining process is simple and clear . One modification of Euclid's axiom has been proposed ...
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Términos y frases comunes
ABCD adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC BC is equal bisected centre circle ABC circumference Constr Construction 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