Euclid's Elements, Βιβλία 1-6;Βιβλίο 11Dent, 1933 - 298 σελίδες |
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Σελίδα 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 ...
Σελίδα 258
... axiom . Many modern editions of Euclid however refer only to the first axiom , as if that alone were sufficient ; a similar remark applies to the demonstrations of I. 15 and I. 24. In these cases we have omitted the reference purposely ...
... axiom . Many modern editions of Euclid however refer only to the first axiom , as if that alone were sufficient ; a similar remark applies to the demonstrations of I. 15 and I. 24. In these cases we have omitted the reference purposely ...
Σελίδα 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 ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal 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 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 shown sides similar and similarly Simson square described square on AC straight line &c straight line AB THEOREM touches the circle triangle ABC triangle DEF twice the rectangle Wherefore whole angle