 | John Playfair - Circle-squaring - 1819 - 350 pages
...rectangles contained by the whole and each of the parts, are together equal to the square of the whole line. Let the straight line AB be divided into any two parts in the point C ; the rectangle AB.BC, together with the rect- » P "R angle AB.AC, is equal to the square... | |
 | Jeremiah Day - Algebra - 1820 - 352 pages
...than in ordinary language. The proposition, (Euc. 4. 2.) that when a straight line is divided into two parts, the square of the whole line is equal to...squares of the two parts, together with twice the product of the parts, is demonstrated, by involving a binomial. Let the side of a square be represented... | |
 | Euclides - 1821 - 294 pages
...are the given quantities : then 6 X 6 -f- 6 X 2 is = to 8 X 8 — 8 X 2. PROP. 4T THEQR. If a right line be divided into any two parts, the square of the whole line is equal to the sum of the squares of the parts and twice the rectangle under the parts On the given line describe... | |
 | 1854 - 1112 pages
...product. Geometry furnishes us with a parallel to both these cases ; for, as Euclid tells us (II., 4), if a straight line be divided into any two parts,...together with twice the rectangle contained by the parts ; and, were we to represent the line as a divided into two parts m, x, the algebraical expression for... | |
 | Charles Tayler - 1824 - 350 pages
...iv. Book ii., viz., that If a number be divided into any two parts, the square of the •whole number is equal to the squares of the two parts, together with twice the product (or rectangle) of the twojiarts. For (c) Prime numbers are such as cannot be represented by... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...CB, together with the square of BC. If therefore a straight line, &c. QED Proposition IV. Theorem. ', If a straight line be divided into any two parts, the square or in* ELEMENTS OP KUCUD. 191 vhole line is equal to the squares of the two parts, together with twice... | |
 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...BCB; therefore AB.BC = AC.CB -f BC3. Therefore, if a straight line, &e. QED C B D E C PROP. IV. THEOR. If a straight line be divided into any two parts,...equal to the squares of the two parts, together with twiee the reetangle eontained by the parts. Let the straight line AB be divided into any two parts... | |
 | Euclid - 1826 - 234 pages
...and it be ag =fg + g2. Q- ED PROPOSITION IV. THEOREM. If a right line be divided into any two part:!, the square of the whole line is equal to the squares...parts, together with twice the rectangle contained under the parts. Let the right line AB be divided into any two parts in the point c ; the square of... | |
 | Jeremiah Day - Algebra - 1827 - 352 pages
...than in ordinary language. The proposition, (Euc. 4- 2.) that when a straight line is divided into two parts, the Square of the whole line is equal to...squares of the two parts, together with twice the product of the parts, is demonstrated, by involving a binomial. Let the side of a square be represented... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C: the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the... | |
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IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 
