 | Great Britain. Committee on Education - 1847 - 606 pagine
...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...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 less than the... | |
 | John Playfair - 1847 - 340 pagine
...PROP. X. PROB. To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line ; it is required to divide if into two equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the... | |
 | Euclides - 1848 - 52 pagine
...made up of the half and the part produced. PROP. XI. PROBLEM. To divide a given straight line into two parts, so that the rectangle contained by the whole...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 of the acute... | |
 | J. Goodall, W. Hammond - 1848 - 390 pagine
...between the perpendicular and the obtuse angle. Section 4. 1. Divide a given straight line into two parts, so that the rectangle contained by the whole...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 of a parallelogram... | |
 | University of Cambridge - 1849 - 560 pagine
...algebraical equations, or any demonstration other than Euclid's ? 3. Divide a given straight line into two parts, so that the rectangle contained by the whole...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 the required manner.... | |
 | Euclid, Thomas Tate - 1849 - 120 pagine
...straight line, &c. QED Again, because EG F is EF PROP. XI. PROB. To divide a given straight line into two parts, so that the -rectangle 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 pagine
...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... | |
 | James Elliot - 1850 - 116 pagine
...the half of its square by § ? 3. Divide 100 into two such parts, that the product of the whole by one of the parts shall be equal to the square of the other part. 4. A horse-dealer bought a number of young horses at a fair, all at the same price, for the sum of... | |
 | Her MAjesty' Inspectors of schools - 1850 - 912 pagine
...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,... | |
 | 582 pagine
...proved in Book 1 and state what ease is omitted. SECTION IT. 1. Divide a given straight line into two parts, so that the rectangle contained by the whole...parts, shall be equal to the square of the other part. 2. If a straight line be divided into any two parts, the square of the whole line is equal to the squares... | |
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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, may be equal to the square of the other part. 
