 | Robert Potts - 1860 - 380 pàgines
...square on BC. If therefore a straight line be divided, &c. QED PROPOSITION IV. THEOREM. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the parts. let the straight... | |
 | Charles Hutton - 1860 - 1020 pàgines
...rectangle AD. AB is equal to the sum of all the oilier rectangles AD. AE, AD.EF, AD.FB. QED Corol. If a right line be divided into any two parts, the square on the > line, is equal to both the rectangles of the wi.ole line and each of th« poti. THEOREM XXXI. The... | |
 | War office - 1861 - 714 pàgines
...side of it are either two right angles or are together equal to two right angles. 2. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts together with twice the rectangle contained by the parts. 3. If in a circle... | |
 | William Grier - 1861 - 316 pàgines
...rectangles of AD and AE, and AD and EF, and AD and FB : thus expressed, AD . AB=AD . AE -f-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. • Instead... | |
 | University of Oxford - 1863 - 316 pàgines
...— a polygon — parallel straight lines. '6* 2. Bisect a given rectilineal angle. 3. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the parts. 4. The complements... | |
 | Euclides - 1864 - 262 pàgines
...square on BC. < If therefore a straight line be divided, &c. QED PROPOSITION IV. THEOREM. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the parts. Let the straight... | |
 | Gerardus Beekman Docharty - 1867 - 474 pàgines
...rectangle AD . AB is equal to the sum of all the other rectangles AD . AE, AD . EF, AD . FB. QE HCorol. If a right line be divided into any two parts, the...rectangles of the whole line and each of the parts. CB THEOREM XXXI. Tlus square of the sum of two lines is greater than the svm of their squares by twice... | |
 | James Maurice Wilson - 1868 - 132 pàgines
...round the point 0 which is determined by the construction above given. EXERCISES. 1. If a straight line be divided into any two parts, the square on the whole line is equal to the sum of the ' rectangles contained by the whole line and each of the parts. 2. Construct a square... | |
 | James Maurice Wilson - 1869 - 260 pàgines
...rectangle AB x .#.#'; and FH is the square on AH; therefore AB x BH= AH*. EXERCISES. 1. If a straight line be divided into any two parts, the square on the whole line will be equal to the sum of the rectangles contained by the whole line and each of the parts. 2. Construct... | |
 | Euclid, Charles Peter Mason - 1872 - 216 pàgines
...preceding proposition is usually incorporated in the proof of the Fourth Proposition. PBOPOSITION IV. If a right line be divided into any two parts, the square on the whole line is equal to the sum of the squares on the parts together with twice the rectangle under the parts. For the construction... | |
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If a straight line be divided into any two parts, the square on the whole line is... 
