| Great Britain. Committee on Education - 1847
...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... | |
| 1847
...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...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... | |
| J. Goodall, W. Hammond - 1848
...triangle between the perpendicular and the obtuse angle. Section 4. 1. Divide a given straight line **into two parts, so that the rectangle contained by...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... | |
| Euclides - 1848
...line 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...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... | |
| University of Cambridge - 1849
...of algebraical equations, or any demonstration other than Euclid's ? 3. Divide a given straight line **into two parts, so that the rectangle contained by...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.... | |
| Elias Loomis - 1849 - 226 páginas
...such that the greater part may be a mean proportional between the whole line and the other part. Let **AB be the given straight line; it is required to divide it into two parts** at the point F, such that AB : AF:: AF:FB. At the extremity of the line AB, erect the perpendicular... | |
| Euclides, Thomas Tate - 1849 - 108 páginas
...wherefore the angles CBD, DBE, and EBA are equal to one another. 2. To trisect a given straight line. Let **AB be the given straight line: It is required to divide it into** three equal parts. Upon AB describe (E. i. 1.) the equilateral triangle ABC; bisect (Ei 9.) the angles... | |
| Great Britain. Committee on Education - 1850
...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... | |
| James Elliot - 1850
...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
...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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