| Euclid, Robert Simson - 1821 - 514 Seiten
...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 Seiten
...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 Hutton - 1822 - 618 Seiten
...up of the four figures, viz. the two squares AF, FD, and the two equal rectangles EF, FB. That is, **the square of AB is equal to the squares of AC, CB,** together with twice the rectangle of AC, CB. ft. ED Corol. Hence, if a line be divided into two equal... | |
| Charles Tayler - 1824 - 350 Seiten
...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 - 1825 - 372 Seiten
...', 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...straight line AB be divided into any two parts in** С ; the square of AB is equnl to the squares of AC, CB, and to twice the rectangle contained by AC,... | |
| Euclid, John Playfair - 1826 - 326 Seiten
...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 Seiten
...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 - 1827 - 332 Seiten
...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 - 1827 - 513 Seiten
...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... | |
| Euclid, Dionysius Lardner - 1828 - 544 Seiten
...rectangle under either of them and a third of the other, #c. #c. PROPOSITION II. THEOREM. (223) If a right **line (AB) be divided into any two parts (in C), the square of** the whole line is equal to the sum of the rectangles under the whole (AB) and each of the parts (AC,... | |
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