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 . ned too frequently, the rt-ctaiiglecontained by two straight lines A B, ACis sometimes simply called the rectangleAB, 4C.] On AB describe the squareADEB ; [I. 46. and through C draw CF parallelto AD or BE. [ Then AE is equal to the rectangles ^-F, AE is the square on AB. And AF is the rectangle contained by BA, AC, for it iscontained by DA, AC, of which DA is equal to BA ; and CE is contained by A B, BC, for BE is equ
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 . ned too frequently, the rt-ctaiiglecontained by two straight lines A B, ACis sometimes simply called the rectangleAB, 4C.] On AB describe the squareADEB ; [I. 46. and through C draw CF parallelto AD or BE. [ Then AE is equal to the rectangles ^-F, AE is the square on AB. And AF is the rectangle contained by BA, AC, for it iscontained by DA, AC, of which DA is equal to BA ; and CE is contained by A B, BC, for BE is equal toAB. Therefore the rectangle AB, AC, together with the rect-angle AB, BC, is equal to the square on AB. Wherefore, if a straight line &c. PROPOSITION 3. THEOREM. If a straight line he divided into any two parts, therectangle contained hy the ichole and one of the parts, isequal to the rectangle contained hy the two parts, togetherwith the square on the aforesaid part. Let the straiglit line AB \)^ divided into any two partsat the point C\ the rectangle AB, BC shall be equal tothe rectangle AC, CB, together with the square on BC. BOOK IL 3, 4. 55. On BC describe the square CDEBproduce ED to F, and through A Adraw A ^parallel to CI) or BE. [ Then the rectangle AEis, equalto the rectangles AD, A E is the rectangle containedby AB, BC, for it is containedby AB, BE, of which BE is equalto BC; and ^Z> is contained by AC, CB, for CD is eaual to CB ;and CE is the square on BC. llierefore the rectangle AB, BC is equal to the rectangleAC, CB, together with the square on BC. Wherefore, if a straight line &c. PROPOSITION 4. a straight line he divided into any two parts, thesquare on the whole line is equal to the squares on the twoparts, together with twice the rectangle contained hy thetwo parts. Let the straight line AB he divided into any two partsat the point C-. the square on AB sliall be equal to thesquares on AC, CB, together with twice the
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Keywords: ., bookcentury1800, booksubjectgeometry, booksubjectmathematicsgree
