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 . BOOK II. 13, 14. 69 and therefore the square on AB is equal to the squareson AC, CB, and twice the rectangle BC, CD. [II. 12, To each of these equals add the square on the squares on AB, BC are equal to the squareon AC, and twice the square on BC, and twice the rect-angle BC, CD. [Axiom because BD is divided into two parts at C, the rect-angle DB, BC is equal to the rectangle BC^ CD and thesquare on BC -, [IL 3
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 . BOOK II. 13, 14. 69 and therefore the square on AB is equal to the squareson AC, CB, and twice the rectangle BC, CD. [II. 12, To each of these equals add the square on the squares on AB, BC are equal to the squareon AC, and twice the square on BC, and twice the rect-angle BC, CD. [Axiom because BD is divided into two parts at C, the rect-angle DB, BC is equal to the rectangle BC^ CD and thesquare on BC -, [IL 3. and the doubles of these are equal, that is, twice the rectangle DB, BC is equal to twice the rectangle BC, CD and twice the square on BC. Therefore the squares on AB, BC are equal to the square on AC, and twice the rectangle DB, BC; that is, the square on A C alone is less than the squares on AB, BC by twice the rectangle DB, BC. Lastly, let the side AC he perpendicularto BC. Then BC is the straight line between theperpendicular and the acute angle at B; and it is manifest, that the squares on AB, BC arc equal to the square on AC, and twice the square on BC
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Keywords: ., bookcentury1800, booksubjectgeometry, booksubjectmathematicsgree
