 | Euclid, John Playfair - 1846 - 334 sider
...(2a+i)2+J2=2o2+2(a+4)2, and the proposition is evident from this algebraical equality. PROP. XI. PROB. To divide a given straight line into two parts, so...rectangle contained by the whole, and one of the parts, may be equal to the square of the other part. Let AB be the given straight line ; it is required to... | |
 | Harvey Goodwin - 1846 - 500 sider
...(l + n) ' ma ' na n (a> + mx) = Ex. 5. Divide the quantity a into two parts such that the product of the whole and one of the parts shall be equal to the square of the other part. Let a? = one part ; .-. a- n' = the other; .-. by the question, ax = (a — at): =... | |
 | 1847 - 508 sider
...angle contained by these two sides is a light angle. SECTION Il. — 1. To divide a straight line, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 2. In every triangle the square of the side subtending either of the acute angles is... | |
 | Great Britain. Committee on Education - 1847 - 606 sider
...the angle contained by these two sides is a right angle. SECTION II. 1. To divide a straight line, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 2. In every triangle the square of the side subtending either of the acute angles is... | |
 | Euclides - 1848 - 52 sider
...the line bisected, and of the square of the line made up of the half and the part produced. PROP. XI. PROBLEM. To divide a given straight line into two...one of the parts, shall be equal to the square of the other part. PROP. XII. THEOREM. In obtuse-angled triangles, if a perpendicular be drawn from either... | |
 | J. Goodall, W. Hammond - 1848 - 390 sider
...line intercepted without the triangle between the perpendicular and the obtuse angle. Section 4. 1. Divide a given straight line into two parts, so that...and one of the parts shall be equal to the square of the other part. 2. Describe a square that shall be double a given triangle. 3. Prove that the diagonals... | |
 | University of Cambridge - 1849 - 560 sider
...upon the necessary homogeneity of algebraical equations, or any demonstration other than Euclid's ? 3. Divide a given straight line into two parts, so that...and one of the parts shall be equal to the square of the other part. Shew that in Euclid's figure four other lines, beside the given line, are divided in... | |
 | Euclid, Thomas Tate - 1849 - 120 sider
...squares of AC, CD: Wherefore, if a straight line, &c. QED Again, because EG F is EF PROP. XI. PROB. To divide a given straight line into two parts, so...contained by the whole, and one of the parts, shall Tie equal to the square of the other part. Let AB be the given straight line; it is required to divide... | |
 | Great Britain. Committee on Education - 1850 - 942 sider
...between the same parallels, are equal to one another. 3. Solve Euc. II. 11. To divide a given finite straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the squire of the other part. 4. Prove Euc. III. 22. The opposite angles of any quadrilateral... | |
 | Her MAjesty' Inspectors of schools - 1850 - 912 sider
...figures, and duplicate ratio. 3. Solve Euc. II. 11. To divide a given finite straight line into two part*, so that the rectangle contained by the whole and one of the parts may be equal to the square of the other jjart. '2. Prove Kuc. 1. 36. Parallelograms upon equal bases,... | |
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To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part. 
