| Jeremiah Day, James Bates Thomson - Algebra - 1848 - 252 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... | |
| Euclides, Thomas Tate - 1849 - 108 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,...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... | |
| John Playfair - Euclid's Elements - 1849 - 317 pages
...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...be divided into any two parts in C ; the square of** AB is equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB, that is, AB2=AC2+CB2+2AC.CB.... | |
| Elias Loomis - Conic sections - 1849 - 226 pages
...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 - School buildings - 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... | |
| Great Britain. Committee on Education - 1850
...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... | |
| JEREMIAH DAY, D.D. LL. D. - 1850
...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... | |
| Charles Davies - Geometry - 1850 - 216 pages
...parts, the square described on the whole line is equivalent to the sum of the squares described on **the two parts, together with twice the rectangle contained by the parts. . Let the** line AB be divided into two n IT n parts at the point E: then will the square described on AB be equivalent... | |
| CHARLES DAVIS, L.L. D. - 1850
...parts, the square described on the whole line is equivalent to the sum of the squares described on **the two parts, together with twice the rectangle contained by the parts. Let the** line AB be divided into two -^ HC parts at the point E : then will the square described on AB be equivalent... | |
| 1852
...to a given triangle, and have one of its angles equal to * Riven rectilineal angle. SECTION II. 1. **If a straight line be divided into any two parts,...together with twice the rectangle contained by the** paits. 2. If a straight line be divided into two equal and also into two unequal parts, the squares... | |
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