Class lessons on Euclid1882 |
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Page 84
... AC = BD . II . To show that AB is || to CD . BC falls on AC and BD and makes ... square , the rhombus , the rhomboid , and the oblong , more generally spoken ... AC , BD , in each case makes the alternate angles equal , and therefore each ...
... AC = BD . II . To show that AB is || to CD . BC falls on AC and BD and makes ... square , the rhombus , the rhomboid , and the oblong , more generally spoken ... AC , BD , in each case makes the alternate angles equal , and therefore each ...
Page 86
... AC = BD , .. opposite sides of gram are equal . II . △ ABC = BCD in area ... square , whose sides and angles are all equal . The rhombus , whose sides ... square and the rectangle , have all their angles right angles . Two , the rhombus ...
... AC = BD , .. opposite sides of gram are equal . II . △ ABC = BCD in area ... square , whose sides and angles are all equal . The rhombus , whose sides ... square and the rectangle , have all their angles right angles . Two , the rhombus ...
Page 104
... AC at right angles to AB ; the angle BAC will form one of the angles of the square , and by cutting off from AC ( produced if necessary ) AD equal to AB we shall obtain another side . Since a square is also a parallelogram , the two ...
... AC at right angles to AB ; the angle BAC will form one of the angles of the square , and by cutting off from AC ( produced if necessary ) AD equal to AB we shall obtain another side . Since a square is also a parallelogram , the two ...
Page 105
... square , and it is described on the given line AB . SUMMARY OF PROPOSITION XLVI . , PROBLEM 14 . On a given straight line to describe a square . Cons . From A draw AC at right angles to AB ; cut off AD = AB . Through B and D draw BE and ...
... square , and it is described on the given line AB . SUMMARY OF PROPOSITION XLVI . , PROBLEM 14 . On a given straight line to describe a square . Cons . From A draw AC at right angles to AB ; cut off AD = AB . Through B and D draw BE and ...
Page 106
... square on BC , and the remaining part , the parallelogram LC , must be equal in area to the square on AC . Now , if you will look at the figure thus ob- tained , you will notice that the line defining the two grams will , if produced ...
... square on BC , and the remaining part , the parallelogram LC , must be equal in area to the square on AC . Now , if you will look at the figure thus ob- tained , you will notice that the line defining the two grams will , if produced ...
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Common terms and phrases
&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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