| Euclides - 1845 - 544 pages
...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 - 434 pages
...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.... | |
| Euclides - 1846 - 292 pages
...rectangle AC, CB, together with the square of BC. Wherefore, If a straight line ScQED PROP. IV. THEOR. If **a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts.** Let the straight line AB be divided into any two parts in C : the square of AB shall be equal to the... | |
| John Playfair - Euclid's Elements - 1846 - 332 pages
...therefore, multiplying both members of this equality by c, we shall have ac=ic+c2. PROP. IV. THEOR. If **a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts.** Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares... | |
| Euclides - 1846 - 272 pages
...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... | |
| Jeremiah Day - Algebra - 1847 - 358 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 - 710 pages
...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 - 52 pages
...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, the...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... | |
| Jeremiah Day, James Bates Thomson - Algebra - 1848 - 264 pages
...concise, 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... | |
| Euclid, Thomas Tate - 1849 - 120 pages
...rectangle AC, CB together with the square of BC. If therefore a straight, &c. QED PROP. IV. THEOR. If **a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts.** Upon AB describe (i. 46.) the square ADEB, and join BD, and through c draw (i. 31.) CGF parallel to... | |
| |