| Euclid, Thomas Tate - 1849 - 108 pages
...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 that the...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
...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... | |
| 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,... | |
| Harvey Goodwin - Mathematics - 1851 - 173 pages
...necessary homogeneity of algebraical equations, or any demonstration other than Euclid's ? 3. Divide **a given straight line into two parts, so that 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 the required manner.... | |
| FRANCIS J. JAMESON - 1851
...(BE2 + CF2) = 4 (ABa + AC2) + 4AE2 + 4AF2, = 4BC2 + AB2 + AC2, = 4BC2 + BC2, - 5BC8. 1849. (A). Divide **a given straight line into two parts, so that the...parts shall be equal to the square of the other part.** (ii. 11.) (B). Shew that in Euclid's figure, four other lines, beside the given line, are divided in... | |
| University of Durham - Education, Higher - 1851
...twice the rectangle contained by the parts. 5. To divide a given straight line into two parts, such **that the rectangle contained by the whole and one...parts shall be equal to the square of the other part.** 6. If two circles cut one another they cannot have the same centre. 7. Equal straight lines in a circle... | |
| JAMES RYAN - 1851
...to divide a line y of 20 inches in length, into two such parts that the rectangle of the whole arid **one of the parts shall be equal to the square of the other.** Ans. 10^/5 — 10, and 30— 10 ^5. 5. It is required to divide the number 60 into two such parts,... | |
| Bengal council of educ - 1852
...which contain the right angle. Is this proposition included in any more general one ? (2.) To divide **a given straight line into two parts, so that the...parts, shall be equal to the square of the other part.** Can this be solved arithmetically ? if so, find approximately into how many parts the given line must... | |
| Euclides - 1852
...equal to the square of the other part. Let AB be the given straight line ; it is required to divide it **into two parts, so that the rectangle contained by...parts, shall be equal to the square of the other part.** Upon AB describe* the square ABDC; • x hi. i. bisect* AC in E, " x . i. and join BE; produce CA to... | |
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