 | Euclides - 1840 - 192 pages
...by the parts. F T» PROP. IV. THEOR. If a straight line (AB) be divided into any two parts (AF, FB), the square of the whole line is equal to the squares of the parts, together with twice the rectangle contained by the parts. Upon AB describe the square ACDB ;... | |
 | John M'Nevin - Arithmetic - 1841 - 300 pages
...like 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...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 - 300 pages
...like 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...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 - 362 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... | |
 | Euclides - Geometry - 1841 - 378 pages
...twice the rectangle contained by the whole and that part, together with the square of the otherpart. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the... | |
 | 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... | |
 | Euclides - 1842 - 316 pages
...rectangles contained by the whole and each of the parts, are together equal to the square of the whole fine. Let the straight line AB be divided into any two parts in the point c ; the rectangle contained by AB, BC, together with the rectangle* AB, AC, shall be equal... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...contained by the whole and each of the parts, are together equal to the square of the whole line. F c B Let the straight line AB be divided into any two parts in the point C ; the rectangle AB.BC, together with the rectangle AB.AC, is equal to the square of AB... | |
 | Scotland free church, gen. assembly - 1847 - 554 pages
...two 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,...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... | |
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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. 
