Class lessons on Euclid1882 |
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Página 148
... . F D - 6 The demonstration is the same as in II . 1 and 2 , making the obvious difference in the construction in accordance with the terms of the enunciation . SUMMARY OF PROPOSITION III . , THEOREM 3 . If 148 CLASS LESSONS ON EUCLID .
... . F D - 6 The demonstration is the same as in II . 1 and 2 , making the obvious difference in the construction in accordance with the terms of the enunciation . SUMMARY OF PROPOSITION III . , THEOREM 3 . If 148 CLASS LESSONS ON EUCLID .
Página 154
... difference + DB . = AB = AD + DB = the difference + 2 DB . Therefore half AB , that is CB = half the difference and DB , and CB = CD + DB . Therefore CD = half of the difference of the two lines . From the construction in the last ...
... difference + DB . = AB = AD + DB = the difference + 2 DB . Therefore half AB , that is CB = half the difference and DB , and CB = CD + DB . Therefore CD = half of the difference of the two lines . From the construction in the last ...
Página 156
... 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 rectangle contained by the ...
... 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 rectangle contained by the ...
Página 159
... difference , and the proposition may be enunciated thus : The square on the difference of two straight lines ( CLASS LESSONS ON EUCLID . 159 PROPOSITIONS 7, 9, AND 10.
... difference , and the proposition may be enunciated thus : The square on the difference of two straight lines ( CLASS LESSONS ON EUCLID . 159 PROPOSITIONS 7, 9, AND 10.
Página 166
... the square on half their difference , is equal to the square on half their sum . Rect . AD , DB and sq . on = sq . on CB . CD Includes Euclid's II . 5 and 6 . II . 8 . If a straight line be di- 166 CLASS LESSONS ON EUCLID .
... the square on half their difference , is equal to the square on half their sum . Rect . AD , DB and sq . on = sq . on CB . CD Includes Euclid's II . 5 and 6 . II . 8 . If a straight line be di- 166 CLASS LESSONS ON EUCLID .
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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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