## Class lessons on Euclid1882 |

### From inside the book

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**equal**to four times the square of the radius , and we shall see that the circle does not quite fill it up ; hence we should expect that the**area**of the circle would be**equal**to rather more than three times the square of the radius . The ... Page 15

... equality of

... equality of

**area**in rectilineal figures . These subjects Euclid discusses in forty - eight propositions ( πpóraσes ) , which are of two kinds , ( 1 ) problems in which he shows how something may be done , e.g. how to describe an ... Page 22

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**equal**to the corresponding side of the other . ( 2 ) In their angles ; each angle of the one must be**equal**to the corresponding angle of the other . ( 3 ) In their**area**, or the space enclosed by the sides . And these three equalities ... Page 23

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**area**or surface . Have we any test of equality which will apply to them all ? Axiom 8 tells us that magnitudes which coincide are**equal**, and , further , it was pointed out in a note that the test of coincidence could be applied to the ... Page 85

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**equal**it will follow that their sides are**equal**, and consequently the whole theorem will be proved . What do we ...**area**, the diameter bisects the parallelogram . Since the sides of the triangles are**equal**, each to each , AC BD ...### 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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