| Jeremiah Day - 1847 - 358 Seiten
...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 - 1847 - 710 Seiten
...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 Seiten
...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 - 1848 - 264 Seiten
...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... | |
| John Playfair - 1849 - 332 Seiten
...parts, the square of the whole line is equal to the squares of the two parts, together with tvtice **the rectangle contained by the parts. Let the straight...CB, and to twice the rectangle contained by AC, CB,** that is, AB2=AC2+CB2+2AC.CB. Upon AB describe (Prop. 46. 1.) the square ADEB, and join BD, and through... | |
| Euclid, Thomas Tate - 1849 - 120 Seiten
...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... | |
| Elias Loomis - 1849 - 252 Seiten
...middle points of the sides which are not parallel. PROPOSITION VIII. THEOREM. If a straight line is **divided into any two parts, the square of the whole line is** equivalent to the squares of the two parts, together with twice the rectangle contained by 'the parts.... | |
| Great Britain. Committee on Education - 1850
...sides which contain the right angle. Section 3. 1. If a straight 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** hy the parts. 2. Show that if a straight line be divided into any two parts, the squares of the whole... | |
| Jeremiah Day - 1850 - 348 Seiten
...language. The proposition, (Euc, 4. 2.) that when a straight line is divided into two parts, tilesquare **of the whole line is equal to the squares of the two parts, together with twice the** product of the parts, is demonstrated, Ijy involving a binomial. Let the side of a square be represented... | |
| Great Britain. Committee on Education - 1850 - 914 Seiten
...makes the alternate angles equal. — Define parallel lines, and alternate angles. 3. If a line be cut **into any two parts, the square of the whole line is equal to the squares of the** parts, and twice the rectangle contained by the parts. — Show the same Algebraically. 4. Prove tluit... | |
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