 If a straight line be divided into any two parts, show that the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part.  Examination Papers for Science Schools and Classes - Page 42by Great Britain. Education Department. Department of Science and Art - 1890Full view - About this book
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...their squares shall be equal to a given square. 13. Divide a given straight line into two parts, such that the squares on the whole line and on one of the parts shall be equal to twice the square on the other part. 14. Any rectangle is the half of the rectangle... | |
 | Euclides - 1862 - 140 pages
...straight line, &c. QED PROPOSITION 7.—THEOREM. If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts,...part, together with the square on the other part. (References—Prop. I. 31, 34, 43, 46; II. 4, cor.) Hypothesis.—Let the straight line AB be divided... | |
 | Euclides - 1864 - 448 pages
...their squares shall be equal to a given square. 13. Divide a given straight line into two parts, such that the squares on the whole line and on one of the parts shall be equal to twice the square on the other part. 15. If a straight line be divided into two equal... | |
 | Euclides - 1864 - 150 pages
...their squares shall be eq^ial to a given square. 13. Divide a given straight line into two parts, such that the squares on the whole line and on one of the parts shall be equal to twice the square on the other part. 15. If a straight line be divided into two equal... | |
 | Euclides - 1864 - 262 pages
...their squares shall be equal to a given square. 13. Divide a given straight line into two parts, such that the squares on the whole line and on one of the parts shall be equal to twice the square on the other part. 14. Any rectangle is the half of the rectangle... | |
 | Queensland. Department of Public Instruction - Education - 1866 - 336 pages
...are 3, 4, and 5 units respectively. 5. Prove that if a straight line be divided into any two parts, the squares on the whole line, and on one of the parts,...part, together with the square on the other part. Give Euclid's demonstration of this proposition ; also, prove it algebraically. 6. Describe a square... | |
 | Euclides - 1865 - 402 pages
...equal to the squares on the two parts, together with twice the rectangle under the parts . n. 4. 4. The squares on the whole line, and on one of the parts, are equal to twice the rectangle under the whole and that part, together with the square on the other part . . . . D. 7. 5. Four times... | |
 | Edinburgh univ - 1866 - 344 pages
...contained by these two sides is a right angle. 12. If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are together equal to twice the rectangle contained by the whole and that part, together with the square... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...square is that which is half of the given square. 504. Divide a given straight line into two parts so that the squares on the whole line and on one of the parts jnay be together double of the square on the other part. 505. Two rectangles have equal areas and equal... | |
 | Euclides - 1871 - 136 pages
...AD,DH QE 1 Aa 7i 7 K. L R PROPOSITION VII. THEOREM. If a straight line- be divided into any two parts, the squares on the whole line and on one of the parts...that part together with the square on the other part. JC Let AB be divided into any two parts in C. Then must tqq. on AB, BC= twice reel. AS, BC together... | |
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