Class lessons on Euclid1882 |
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Página 16
... PROP . I. Having now cleared the way , we can enter upon the discussion of the first proposition , which is a problem , that is , it shows how something is to be done . We are ' required to describe an equilateral triangle on a given 16 ...
... PROP . I. Having now cleared the way , we can enter upon the discussion of the first proposition , which is a problem , that is , it shows how something is to be done . We are ' required to describe an equilateral triangle on a given 16 ...
Página 18
... AC and BC . ABC is the △ required . B C. Proof ( Direct ) .- ACAB ( def . 15 ) . } = .. BC AC ( ax . 1 ) , and △ ABC is equilateral , & c . = Q.E.D. Prop . II . We pass on to the second 18 CLASS LESSONS ON EUCLID .
... AC and BC . ABC is the △ required . B C. Proof ( Direct ) .- ACAB ( def . 15 ) . } = .. BC AC ( ax . 1 ) , and △ ABC is equilateral , & c . = Q.E.D. Prop . II . We pass on to the second 18 CLASS LESSONS ON EUCLID .
Página 19
... Prop . 1. He tells us to draw a straight line from A to B and on it describe an equilateral triangle ( I. 1 ) , C and to produce its sides DA and DB through the circle already drawn to any points E and F. This gives the key to the ...
... Prop . 1. He tells us to draw a straight line from A to B and on it describe an equilateral triangle ( I. 1 ) , C and to produce its sides DA and DB through the circle already drawn to any points E and F. This gives the key to the ...
Página 24
... Prop . V. Before beginning the next theorem , I wish you to notice that from Proposition IV . we learn ( 1 ) that triangles are equal in all respects , if in each triangle two sides and the angle between them are severally equal ...
... Prop . V. Before beginning the next theorem , I wish you to notice that from Proposition IV . we learn ( 1 ) that triangles are equal in all respects , if in each triangle two sides and the angle between them are severally equal ...
Página 29
... 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.
... 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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alternate angles angles are equal angles equal apply base bisected Book called Cheaper Edition circle coincide common cons construction demonstration Demy 8vo describe diameter difference divided double draw drawn English equal equilateral triangle Euclid exterior fall Fcap figure follows four given line given point given straight line gram greater Illustrations interior angles isosceles triangle Join Large LECTURE less meet method opposite opposite angles opposite sides pair parallel parallelogram perpendicular Poems Portrait problem produced proof Prop PROPOSITION prove rect rectangle contained remaining right angles Second Edition sides Small crown 8vo square square on half SUMMARY OF PROPOSITION THEOREM Translated triangle triangle ABC twice unequal vols Wherefore whole line
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