 | John Playfair - 1819 - 317 pages
...if a straight If D -E line, &c. Q, ED PROP. IV. THEOR. If a straight line be divided into any tiio parts, the square, of the whole line is equal to the...together with twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts in C ; Uie square of AB is equal to the squares... | |
 | John Mason Good - 1819 - 740 pages
...rectangle contained by the two parts, together with tiie square of the furesaicl part. Prop. IV. Theor. If a straight line be divided into any two parts, the square of the whole line n equal to the squares of the two parts, together with twice the rectangle contained by the parts.... | |
 | Jeremiah Day - Algebra - 1820 - 332 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... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...BC. If therefore a straight line, &c. QED PROP. IV. THEOR. IP a straight line be divided into any twq parts, the square of the whole line is equal to the squares of the two pai ts, together with twice the rectangle contained by the parts. Let the straight line AB be divided... | |
 | 1854 - 1110 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, the...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 - 372 pages
...', 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 the rectangle contained by the parts. Let the straight line AB be divided into any two parts in С ; the square of AB is equnl to the squares... | |
 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...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, the...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 - 236 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... | |
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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. 
