Class lessons on Euclid1882 |
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Página 107
... side of the square on BC and the line AD joining their extremities . Then taking FB , BC and joining FC we shall obtain a triangle similar to ABD . About this triangle we must answer two questions . ( 1 ) Is it half of the square on BA ...
... side of the square on BC and the line AD joining their extremities . Then taking FB , BC and joining FC we shall obtain a triangle similar to ABD . About this triangle we must answer two questions . ( 1 ) Is it half of the square on BA ...
Página 150
... square on AB is divided are together equal to the squares on AC , CB , and twice the rectangle AC , CB.-Q.E.D. Again ... half the line . ' square = twice Since the line is divided into two 150 CLASS LESSONS ON EUCLID .
... square on AB is divided are together equal to the squares on AC , CB , and twice the rectangle AC , CB.-Q.E.D. Again ... half the line . ' square = twice Since the line is divided into two 150 CLASS LESSONS ON EUCLID .
Página 151
... square on half the line , and twice the rectangle contained by the parts = twice the square on half the line ; that is , the square on the whole line = four times the square on half the line . SUMMARY OF PROPOSITION IV . , THEOREM 4 ...
... square on half the line , and twice the rectangle contained by the parts = twice the square on half the line ; that is , the square on the whole line = four times the square on half the line . SUMMARY OF PROPOSITION IV . , THEOREM 4 ...
Página 154
Marianne Nops. It remains to construct the square on half the difference of the two straight lines . Now AD the difference + DB . = AB = AD + DB = the difference + 2 DB . Therefore half AB , that is CB = half the difference and DB , and ...
Marianne Nops. It remains to construct the square on half the difference of the two straight lines . Now AD the difference + DB . = AB = AD + DB = the difference + 2 DB . Therefore half AB , that is CB = half the difference and DB , and ...
Página 156
... square on half their difference = the square on half their sum . Rect . AD , DB and sq . on CD = sq . on CB . EUCLID'S ENUNCIATION II . 5 . If a straight line be divided into two equal parts and also into two unequal parts , the ...
... square on half their difference = the square on half their sum . Rect . AD , DB and sq . on CD = sq . on CB . EUCLID'S ENUNCIATION II . 5 . If a straight line be divided into two equal parts and also into two unequal parts , the ...
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Términos y frases comunes
&c.-Q.E.D. PROPOSITION ABCD alternate angles angle ABC angle ACB angles are equal angles equal base BC bisected Cheaper Edition circle cons construction Demy 8vo diameter enunciation equal bases equal in area equal sides equal triangles equilateral triangle Euclid exterior Fcap Frontispiece given angle given line given point given straight line given triangle gnomon gram half the line Illustrations interior and opposite interior angles isosceles triangle Join line equal meet opposite angles opposite sides parallelogram perpendicular Poems problem produced proof Prop rectangle contained rhombus right angles right-angled triangle Second Edition sides equal Small crown 8vo square on AC square on half SUMMARY OF PROPOSITION THEOREM Third Edition Translated triangle ABC triangles are equal twice the rect twice the rectangle vertical angle vols Wherefore whole line
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