Class lessons on Euclid1882 |
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Сторінка 11
... joining the opposite angles of any quadrilateral is called a diameter , or diagonal . Parallelograms are of four kinds , which are thus defined by Euclid : - 6 : - 30. A square is that which has all its sides equal and all its angles ...
... joining the opposite angles of any quadrilateral is called a diameter , or diagonal . Parallelograms are of four kinds , which are thus defined by Euclid : - 6 : - 30. A square is that which has all its sides equal and all its angles ...
Сторінка 18
... Join AC and BC . ABC is required . C. the Proof ( Direct ) .- .— AC = BC = } A AB ( 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 .
... Join AC and BC . ABC is required . C. the Proof ( Direct ) .- .— AC = BC = } A AB ( 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 .
Сторінка 20
... Join AB , and on it de- scribe the equilateral A DAB . With radius BC draw circle GCH . Produce DB to meet it in G. With radius DG draw circle GKL , produce DA to meet it in L. Proof- DL = DG ( def . 15 ) . DA = DB ( def . 24 ) ...
... Join AB , and on it de- scribe the equilateral A DAB . With radius BC draw circle GCH . Produce DB to meet it in G. With radius DG draw circle GKL , produce DA to meet it in L. Proof- DL = DG ( def . 15 ) . DA = DB ( def . 24 ) ...
Сторінка 27
... join FC , GB . = Proof . - By I. 4 prove ( 1 ) the larger pair of triangles equal , ( 2 ) the smaller pair of triangles equal . 6 Since the smaller As contain the s on the other side of the base , ' these angles are equal . F D L G E ...
... join FC , GB . = Proof . - By I. 4 prove ( 1 ) the larger pair of triangles equal , ( 2 ) the smaller pair of triangles equal . 6 Since the smaller As contain the s on the other side of the base , ' these angles are equal . F D L G E ...
Сторінка 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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&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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