| John M'Nevin - Arithmetic - 1841 - 300 pages
...manner 22 = 2 x 10 = 20+ 2 = 2 tens and 2 over. Hence, from the properties of Euclid. 4, Lib. 2. "If **a straight line be divided into any two parts the...with twice the rectangle contained by the parts."** Thus, let AB be divided into two parts, 6 equal to 6 squared plus 4 squared, together with twice the... | |
| John M'Nevin - Arithmetic - 1841 - 280 pages
...manner 22 = 2 x 10= 20 + 2 = 2 tens and 2 over. Hence, from the properties of Euclid. 4, Lib. 2. "If **a straight line be divided into any two parts the...with twice the rectangle contained by the parts."** Thus, let AB be divided into two parts, 6 and 4, the square of the whole line 10, which is 100, is... | |
| Jeremiah Day - Algebra - 1841 - 364 pages
...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 the squares of the two parts, together with** tv/ice the product of the parts, is demonstrated, by involving a binomial. Let the side of a square... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...: therefore, multiplying both members of this equality by c, we shall have ac= 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 - 1842 - 320 pages
...AC, cв, together with the square of вc. If therefore a straight line, &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.** Let the straight line AB be divided into any two parts in c : the square of AB is equal to the squares... | |
| William Grier - Mechanical engineering - 1842 - 320 pages
...and AE, and AD and EF, and AD and FB: thus expressed, AD . AB=AD . AE +AD . EF+AD . FB.* If a right **line be divided into any two parts, the square of the whole line, is equal to** both the rectangles of the whole line and each of the parts. 30. Let the line AB be the sum of any... | |
| Scotland free church, gen. assembly - 1847 - 552 pages
...right angles. 3. Parallelograms upon equal bases, and between the same parallels, are equal. 4. If **a straight line be divided into any two parts, the...square of the whole line is equal to the squares of** each of the parts together with twice the rectangle contained by the parts. 5. Equal straight lines... | |
| James Bates Thomson - Algebra - 1844 - 266 pages
...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... | |
| Euclid - Geometry - 1845 - 218 pages
...together with the square of BC. If therefore a straight line, &c. QED PROPOSITION IV. THEOB. — 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... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...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...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... | |
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