| Euclid - Geometry - 1853 - 176 pages
...together with the rectangle under the two parts. {The square on the whole line is equal in area to the sum of the squares on the parts, together with twice the rectangle under the parts. 'The sum of the square on the whole line and the square on either segment is equal... | |
| Euclides - 1860 - 288 pages
...the rectangle AC • CB. PROPOSITION IV. THEOREM. If a straight line be divided into any two parts, the square on the whole line is equal to the sum of the squares on the two parts, together with twice the rectangle contained by the parts. Given the straight... | |
| James Maurice Wilson - Geometry - 1868 - 132 pages
...same parallels. ELEMENTARY GEOMETRY. THEOREM 25. If a straight line is divided into any two parts, the square on the whole line is equal to the sum of the squares on the parts and twice the rectangle contained by the parts. Let AB be divided in C. Describe... | |
| Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...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 employed... | |
| Edward Atkins - 1874 - 426 pages
...straight line, <fec. QED Proposition 4. — Theorem. If a straight line be divided into any two parts, the square on the whole line is equal to the sum of the squares on the two parts, together with twice the rectangle contained by the parts. Let the straight... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...rectangle BC,PQ + rectangle BC, QC. Hence, if a straight line be divided into cuiy number of parts, the square on the whole line is equal to the sum of the rectangles contained by the whole line and the several parts. COR. 2. If A be = one of the parts of... | |
| Robert Potts - Geometry - 1876 - 446 pages
...triangle. 9. If a straight line be divided into two parts, the square on the whole line is equal to the squares on the parts, together with twice the rectangle contained by the parts. 10. In every triangle, the square on the side subtending an acute angle is less than the squares on... | |
| Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...lines joining the middle points of opposite sides. 49. If a straight line be divided into three parts, the square on the whole line is equal to the sum of the squares on the parts together with twice the rectangle contained by each two of the parts. 50. Given... | |
| Edward Atkins - 1876 - 130 pages
...straight line, &c. QED Proposition 4.— Theorem. If a straight line be divided into any two parts, the square on the whole line is equal to the sum of the squares on the two parts, together with twice the rectangle contained by the parts. Let the straight... | |
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