| John Playfair - Circle-squaring - 1819 - 333 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 - 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
...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
...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
...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
...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 - 320 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 - 180 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 - 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... | |
| Robert Simson - Trigonometry - 1827 - 513 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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