 | Harvey Goodwin - Mathematics - 1846 - 500 pages
...(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): = o2 - Zax + a?2, x- -... | |
 | John Playfair - Euclid's Elements - 1847 - 340 pages
...6)2; hence, (2a-t-6)2+62=2a2+2(a+6)2, and the proposition is evident from this algebraical equality. PROP. XI. PROS. To divide a given straight line into...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... | |
 | Great Britain. Committee on Education - School buildings - 1847 - 606 pages
...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... | |
 | Education - 1847 - 508 pages
...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... | |
 | Euclides - 1848 - 52 pages
...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 parts, so...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 pages
...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...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 pages
...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...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 pages
...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 pages
...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 - 116 pages
...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... | |
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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. 
