Euclid's Elements, Βιβλία 1-6;Βιβλίο 11Dent, 1933 - 298 σελίδες |
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Σελίδα 13
... impossible . But if one of the vertices as D , be within the other triangle ACB , produce AC , AD to E , F. Then because AC is equal to AD , in the triangle ACD , [ Hyp . the angles ECD , FDC , on the other side of the base CD , are ...
... impossible . But if one of the vertices as D , be within the other triangle ACB , produce AC , AD to E , F. Then because AC is equal to AD , in the triangle ACD , [ Hyp . the angles ECD , FDC , on the other side of the base CD , are ...
Σελίδα 89
... impossible . [ I. 17 . Therefore the straight line drawn from A at right angles to AB does not fall within the circle . And in the same manner it may be shown that it does not fall on the circumference . Therefore it must fall without ...
... impossible . [ I. 17 . Therefore the straight line drawn from A at right angles to AB does not fall within the circle . And in the same manner it may be shown that it does not fall on the circumference . Therefore it must fall without ...
Σελίδα 151
... impossible . 시 B | C F [ Construction . [ V. Definition 5 . [ Construction . Therefore A and B are not unequal ; that is , they are equal . Next , let C have the same ratio to A and B ; A shall be equal to B. For , if A is not equal to ...
... impossible . 시 B | C F [ Construction . [ V. Definition 5 . [ Construction . Therefore A and B are not unequal ; that is , they are equal . Next , let C have the same ratio to A and B ; A shall be equal to B. For , if A is not equal to ...
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