The Public School Euclid and Algebra . PROPOSITION 2. Problem. From a given point to draw a straight line equai. to a givenstraight Let A be the given point, and BC the given straight is required to draw from A a straight line equal to BC. Join AB. Post. 1. On AB describe the equilateral ^ DAB. Prop. 1 With centre B and distance BC describe 0 CEF. Post. 3. Produce DB to meet the O*^^ CEF in E. Post. 2. With centre D and distance DE describe 0 EGH. Post. 3. Produce DA to meet the O^*^ ECU in G. Post. 2. EUCLIDS ELEMENTS. 11 Then will ^6^ = , because D is the centre of 0 EG
The Public School Euclid and Algebra . PROPOSITION 2. Problem. From a given point to draw a straight line equai. to a givenstraight Let A be the given point, and BC the given straight is required to draw from A a straight line equal to BC. Join AB. Post. 1. On AB describe the equilateral ^ DAB. Prop. 1 With centre B and distance BC describe 0 CEF. Post. 3. Produce DB to meet the O*^^ CEF in E. Post. 2. With centre D and distance DE describe 0 EGH. Post. 3. Produce DA to meet the O^*^ ECU in G. Post. 2. EUCLIDS ELEMENTS. 11 Then will ^6^ = , because D is the centre of 0 EGH, .. DE = DG. Def. o/(^. Of these, the parts Z)^ and i) ^4 are equal. Def. of equilateral /\.the remainders £E and AG are equal. Ax. 3. And, because J5 is the centre of 0 CEF, .-. BC = BE. D^f. o/Q But AG = AG = BC. Ax. 1. Thus from the point A a straight line AG has been drawnequal to BC. QUESTIONS ox PROPOSITION 2. L Under what circumstances would the point D lie outside of thecircle CEF ? On the circumference of the circle CEF ? 2. If D were without the circle CEF, would it be necessary to produce BB ? 3. Could the problepublicschoolwest00auth
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