| FRANCIS J. JAMESON - 1851
.../. 4 (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...and one of 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,... | |
| Harvey Goodwin - 1851 - 173 páginas
...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... | |
| ...every respect." Enumerate tlie cases proved in Book 1 and state what ease is omitted. SECTION IT. 1. **Divide a given straight line into two parts, so that...one of the 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... | |
| University of Durham - 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 of the 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... | |
| Euclides - 1852
...and part produced (25). These two Propositions may be omitted at the first reading.] PEOP. XL PROB. **To divide a given straight line into two parts, so...one of the parts, shall be 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... | |
| Bengal council of educ - 1852
...two sides 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...one of 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... | |
| Charles Astor Bristed - 1852
...every triangle are equal to two right angles. 3. Divide a given straight line into two such parts, **that the rectangle contained by the whole and one of the parts shall be equal to the square of** the other part. 4. The angle at the centre of a circle is double of the angle at the circumference,... | |
| 1852
...two sides 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 rectangle contained** hy the whole and one of the parts, shall be equal to the square of the other part. Can this be solved... | |
| Euclides - 1853
...of AD, DB, are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED 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. Let AB be the given straight line ; it is required to divide it into two parts, so... | |
| Royal Military Academy, Woolwich - 1853
...are double of the squares of AC, CD. Wherefore, if a straight line, etc. QED PROPOSITION XI. PROB. **To divide a given straight line into two parts, so...one of the parts, shall be equal to the square of** the other part. Upon AB describe (46. i.) the square ABDC ; bisect (10. i.) AC in E, and join BE ;... | |
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