| Euclid, James Thomson - Geometry - 1845 - 352 pages
...equal to the square of BC, together with the rectangle AC.CB.* If, therefore, &c. PROP. IV. THEOR. — **If a straight line be divided into any two parts,...the squares of the two parts, together with twice** their rectangle, t Let the straight line AB be divided into any two parts in C ; the square of AB is... | |
| Euclides - 1845
...line is equal to four times the square of half the line. Also, if a line be divided into any three **parts, the square of the whole line is equal to the squares of the** three parts, and twice the rectangle contained by every two parts. Prop. iv. Algebraically, (fig. Prop,... | |
| Scottish school-book assoc - 1845
...two parts in the point C, the proposition becomes the following. If a straight line be divided into **two parts, the square of the whole line is equal to the** sum of the squares of the parts, together with twice the rectangle contained by the parts. Cor. 2.... | |
| Euclid - Geometry - 1845 - 199 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 are equal to twice the rectangle AB, BC, together with the square... | |
| Euclides - 1846
...under AC and CF. PROPOSITION IV. THEOREM. If a right line (AB) be divided into any two parts, (in O) **the square of the whole line is equal to the squares of the** parts, together with twice the rectangle under the parts. On AB describe the square ACDB, and draw... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 317 pages
...contained by the whole and each of the parts, are together equal to the square of the whole line. c B **Let the straight line AB be divided into any two parts in** the point C ; the rectangle AB.BC, together with the rectangle AB.AC, is equal to the square of AB... | |
| Euclides - 1846
...equal to the rectangle contained by the two parts, together with the square of the aforesaid part, **Let the straight line AB be divided into any two parts in** the point C : the rectangle AB, BC shall be equal to the rectangle AC, CB, together with the square... | |
| Jeremiah Day - Algebra - 1847 - 332 pages
...than in ordinary language. The proposition, (Euc. 4. 2.) that when a straight line is divided into **two par.ts, the square of the whole line is equal...squares of the two parts, together with twice the** product of the parts, is demonBtrated, by involving a binomial Let the side of a square be represented... | |
| Great Britain. Committee on Education - School buildings - 1847
...triangle. 3. A straight line being divided into two parts, prove the square of the whole line to be **equal to the squares of the two parts, together with twice the rectangle contained by the parts.** 4. Prove the angle in a semicircle to be a right angle. 518 mities 36° 201 and 60° 10* ; required... | |
| Euclides - 1848
...rectangle contained by the two parts, together with the square of the aforesaid part. PROP. IV. THEOREM. **If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts.** COR. From the demonstration, it is manifest, that the parallelograms about the diameter of a square... | |
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