Class lessons on Euclid1882 |
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Side 13
... con- tinually produced , shall at length meet upon that side on which are the angles which are together less than two right angles . ' THE AXIOMS . We next have a list of nine axioms , in the original kowal Evvoial , common notions ...
... con- tinually produced , shall at length meet upon that side on which are the angles which are together less than two right angles . ' THE AXIOMS . We next have a list of nine axioms , in the original kowal Evvoial , common notions ...
Side 16
... con- secutively . A line is usually named by two letters placed at its extremities , thus the line AB ab , an angle by three , placing the letter at the angular point in the middle , thus the angle ABC or CBA . A rectilineal figure ...
... con- secutively . A line is usually named by two letters placed at its extremities , thus the line AB ab , an angle by three , placing the letter at the angular point in the middle , thus the angle ABC or CBA . A rectilineal figure ...
Side 18
... Cons . With common radius AB , describe circles from centres A and B. These will cut at point Join AC and BC . ABC is required . C. the Proof ( Direct ) .- .— AC = BC = } A AB ( def . 15 ) . .. BC = AC ( ax . 1 ) , and △ ABC is ...
... Cons . With common radius AB , describe circles from centres A and B. These will cut at point Join AC and BC . ABC is required . C. the Proof ( Direct ) .- .— AC = BC = } A AB ( def . 15 ) . .. BC = AC ( ax . 1 ) , and △ ABC is ...
Side 20
... Cons . - 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 ) ...
... Cons . - 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 ) ...
Side 21
... Cons . - Make line AD = C ( I. 2 ) . Draw circle DEF , cutting AB at E. Proof . - AE AD C ( def . 15 , = = cons . ax . 1 ) . B E F C Α D This proposition concludes the first group of problems , by which we have learnt to do three things ...
... Cons . - Make line AD = C ( I. 2 ) . Draw circle DEF , cutting AB at E. Proof . - AE AD C ( def . 15 , = = cons . ax . 1 ) . B E F C Α D This proposition concludes the first group of problems , by which we have learnt to do three things ...
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Almindelige termer og sætninger
&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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