## Class lessons on Euclid1882 |

### From inside the book

Results 6-10 of 26

Page 15

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**circles**, & c . , which are to be drawn in order to solve the problem or demonstrate the theorem . Sometimes , however , no construction is re- quired . The proof shows by reasoning that the problem proposed has CLASS LESSONS ON EUCLID ... Page 17

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**circle**may be described from any centre at any distance from that centre . ' Let us refer to the definition of a**circle**( def . 15 ) . It is to the latter part that I wish to draw your attention , ' and is such that all straight lines ... Page 18

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**circles**cut one another , which we will call C and D , and at each of these , two radii , one drawn from the centre of each**circle**( i.e. from A and B ) , would meet . Take the point C and draw lines AC and BC from points A and B ( post ... Page 19

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**circle**of which it forms a radius , so that by taking BC as radius of a**circle**we can draw any number of lines equal to it , from the centre of the**circle**. Draw this**circle**, taking B as its centre . Now sup- posing the point A should ... Page 20

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**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 ) . .. remainder AL = BG = BC ( ax . 3 , def . 15 ) . Proposition III . is also a ...### Other editions - View all

### 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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