| Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...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 - Euclid's Elements - 1827 - 246 pages
...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 - Geometry - 1837 - 410 pages
...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 - Geometry - 1845 - 380 pages
...(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 - Education, Higher - 1851
...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 - Mathematics - 1853 - 472 pages
...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
...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
...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
...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 - Euclid's Elements - 1867 - 426 pages
...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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