 | Daniel Cresswell - 1819 - Liczba stron: 446
...(Constr.) AB is to AD in the given ratio ; . -. PQ is to PR in the given ratio. PROP. XLII. 51. PROBLEM. To divide a given straight line into two parts, such,...have a given ratio to the square of the other part. Let AB be the given straight line : It is reA r, quired to divide it into two parts, such that the... | |
 | Daniel Cresswell - 1825 - Liczba stron: 616
...(constr.) AB is to AD in the given ratio ; ... PQ is to PR in the given ratio. PROP. XLII. 51. PROBLEM. To divide a given straight line into two parts, such, that the rectangle contained by the whole tine and out; of Us parts, shall have a given ratio to the square of the other part *. Let Jli be the... | |
 | John Radford Young - 1827 - Liczba stron: 246
...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 - Liczba stron: 410
...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 - Liczba stron: 382
...(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 - Liczba stron: 222
...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 - Liczba stron: 474
...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 - Liczba stron: 270
...they meet the circumference, are together equal to the square of the diameter. PROP. I)- PROBLEM — 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.... | |
 | Euclides - 1858 - Liczba stron: 248
...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 - Liczba stron: 332
...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,... | |
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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. 
