 | Daniel Cresswell - 1817 - 454 pagina’s
...AB at the circumference of the given circle DPE. PROP. XXIV. 114. Problem. To divide a given finite straight line into two parts, such that the rectangle, contained by the whole line and one of the parts, shall most exceed the square of that part. Let AB be the given finite straight line ; it... | |
 | John Radford Young - 1827 - 246 pagina’s
...which it is included, without violating one of the most obvious rules of logic. PROPOSITION XXXII. PROBLEM. To divide a given straight line into two parts, such that the greater part may be a mean proportional between the whole line and the other part. Let AB be the proposed... | |
 | Euclid, James Thomson - 1837 - 410 pagina’s
...the lines forming a given angle, to draw a straight line cutting off the least possible triangle. 40. To divide a given straight line into two parts, such that the square of one of them may be double of the square of the other, or may be in any given ratio to it.... | |
 | Euclid, James Thomson - 1845 - 382 pagina’s
...(I. 47) equal to the squares of GA, AM, the sides of the hexagon and decagon. PROP. XXII. PROB. — To divide a given straight line into two parts, such that the square of one of them may be equal to the rectangle contained by the other, and a given straight line.... | |
 | University of Durham - 1851 - 222 pagina’s
...line is equal to the square of the parts together with 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... | |
 | Royal Military Academy, Woolwich - 1853 - 476 pagina’s
...both are answers to 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... | |
 | Euclides - 1855 - 270 pagina’s
...will bo the greatest possible when the segments of the given straight line are equal. PROP. XXVIII. PROBLEM. To divide a given straight line into two parts such that of the two parallelograms having the same altitude described upon tliem, one may be similar to a given... | |
 | Euclides - 1858 - 248 pagina’s
...figure ABED is the square required. (46. I.) PBOB. 15. To divide a given line, AB, into two parts, so that the rectangle contained by the whole line and one of its parte, AB-BH, Khali be equal to the square of the other part, AH. On AB, by 46. 1. , describe the square... | |
 | Royal college of surgeons of England - 1860 - 332 pagina’s
...bisected, shall be equal to the square of the straight line made up of the half and the part produced. 8. Divide a given straight line into two parts, such...the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. PRELIMINARY GENERAL EXAMINATION. Christmas,... | |
 | Euclid, Isaac Todhunter - 1867 - 426 pagina’s
...parts is equal to the sum of the squares described on the parts, the straight line is bisected. 135. Divide a given straight line into two parts such that the rectangle contained by them shall be the greatest possible. 136. Construct a rectangle equal to the difference of two given... | |
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Divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part. 
