| 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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