 | 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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If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 
