The elements of Euclid for the use of schools and colleges : comprising the first two books and portions of the eleventh and twelfth books; with notes and exercises . the centre B, at the dis-tance BC, describe the circleCGH, meeting DFat G. [Post. the centre D, at the dis-tance DG, describe the circleGKL, meeting Z>^at Z. [Post. shall be equal to BC. Because the point B is the centre of the circle CGIT^ BGis eqnul to BG. [Definition 15. And because the point D is the centre of the circle GKL^DL is equal to DG; [Definition. 15. and DA, DB parts of them are equal; [Definit
The elements of Euclid for the use of schools and colleges : comprising the first two books and portions of the eleventh and twelfth books; with notes and exercises . the centre B, at the dis-tance BC, describe the circleCGH, meeting DFat G. [Post. the centre D, at the dis-tance DG, describe the circleGKL, meeting Z>^at Z. [Post. shall be equal to BC. Because the point B is the centre of the circle CGIT^ BGis eqnul to BG. [Definition 15. And because the point D is the centre of the circle GKL^DL is equal to DG; [Definition. 15. and DA, DB parts of them are equal; [Definition 24. therefore the remainder ^Z is equal to the remainderBG. [Axiom, 3. But it has been shewn that BC is equal to BG ;therefore AL and ^Care each of them equal to things which are eciual to the same thing are equal toone another. [Axiom 1. Therefore ^Z is equal to BO. Wherefore from the given point A a straight line Althas been drawn equal to the given straight line BG. PROPOSITION 3. the greater of tico given straight lines to cut offa part equal to the less Let AB and C be the two given straight lines, of which BOOK I. 3, 4. 9. AB is the greater : it is required to cut off from AB, thogreater, a part equal to C the less. From the point A drawthe straight line AD equalto C; [I. 2. and from the centre A, atthe distance AD, describethe circle DEF meeting ABat E. [Postulate 3. AE shall be equal to C. Because the point A is tho centre of the circle DEF,AE is equal to AD. [Dejinition 15, But C is equal to AD. [Construction. Therefore AE and Care each of them equal to AE is equal to C. [Axiom 1, Wherefore from AB the greater of two given straightlines a part AE has been cut off equal to C the less. PEOPOSITION 4. THEOREM. If two triangles have two sides of the one equal to twosides of the other, each to each, and have also the anglescontained hy those sides equal to one another, they shallalso hare their bases or third sides equal; a
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Keywords: ., bookcentury1800, booksubjectgeometry, booksubjectmathematicsgree
