Class lessons on Euclid1882 |
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Seite 10
... unequal sides ; ( 2 ) according to their angles , as right - angled , obtuse - angled , and acute - angled . It will be shown further on that every triangle contains two acute angles ; consequently a right - angled triangle has 10 CLASS ...
... unequal sides ; ( 2 ) according to their angles , as right - angled , obtuse - angled , and acute - angled . It will be shown further on that every triangle contains two acute angles ; consequently a right - angled triangle has 10 CLASS ...
Seite 11
... unequal sides . ' 6 27. A right - angled triangle is that which has a right angle . ' 28. ' An obtuse - angled triangle is that which has an obtuse angle . ' 29. An acute - angled triangle is that which has three acute angles . ' OF ...
... unequal sides . ' 6 27. A right - angled triangle is that which has a right angle . ' 28. ' An obtuse - angled triangle is that which has an obtuse angle . ' 29. An acute - angled triangle is that which has three acute angles . ' OF ...
Seite 13
... unequal . ' 5. ' If equals be taken from unequals the remainders are unequal . ' If A = C but B and D represent unequal magnitudes , then A + B is not equal to C + D . 8. ' Magnitudes which coincide or exactly fill the same space are ...
... unequal . ' 5. ' If equals be taken from unequals the remainders are unequal . ' If A = C but B and D represent unequal magnitudes , then A + B is not equal to C + D . 8. ' Magnitudes which coincide or exactly fill the same space are ...
Seite 24
... unequal side . The point opposite the base , at which the other two sides of a triangle meet , is called the ' vertex , ' and the angle at this point the ' vertical angle . ' Prop . V. Before beginning the next theorem , I wish you to ...
... unequal side . The point opposite the base , at which the other two sides of a triangle meet , is called the ' vertex , ' and the angle at this point the ' vertical angle . ' Prop . V. Before beginning the next theorem , I wish you to ...
Seite 29
... . 3 ) , join DC . Proof ( Indirect ) .- Show that △ DBC = △ ABC ( I. 4 ) . This is absurd ( ax . 9 ) . .. AB is not unequal to AC , i.e. AB = c AC . LECTURE V. PROPS . 7-8 . - RESULTS OBTAINED FROM CLASS LESSONS ON EUCLID . 29.
... . 3 ) , join DC . Proof ( Indirect ) .- Show that △ DBC = △ ABC ( I. 4 ) . This is absurd ( ax . 9 ) . .. AB is not unequal to AC , i.e. AB = c AC . LECTURE V. PROPS . 7-8 . - RESULTS OBTAINED FROM CLASS LESSONS ON EUCLID . 29.
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&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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