 To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.  Euclid - Page 138by Euclid, Rupert Deakin - 1903 - 164 pagesFull view - About this book
 | Harvey Goodwin - Mathematics - 1851 - 196 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 the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. Shew that in Euclid's figure four... | |
 | Francis James Jameson - Mathematics - 1851 - 144 pages
.../. 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 the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. (ii. 11.) (B). Shew that in Euclid's... | |
 | 1867 - 336 pages
...be less than twice their rectangle. 3. If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight liue which is made... | |
 | Euclides - 1852 - 152 pages
...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 that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Let AB be the given straight... | |
 | Bengal council of educ - 1852 - 348 pages
...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 by the whole and one of the parts, shall be equal to the square of the other part. Can this be solved arithmetically... | |
 | Education - 1852 - 478 pages
...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 - 146 pages
...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...parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part. Let AB be the given straight... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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 that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. Upon AB describe (46. i.) the... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 476 pages
...the question in its literal meaning. 2. To divide a line of 20 inches in length into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Let x = the greater part ; then 20 — x = the less... | |
 | Euclides - Geometry - 1853 - 334 pages
...AC, CD. Which was to be proved. PEOP. XI. PEOB. To divide a given straight line into two such parts, that the rectangle contained by the whole line and 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... | |
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