 | Daniel Cresswell - 1819 - 446 σελίδες
...(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 - 616 σελίδες
...(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 - 246 σελίδες
...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 σελίδες
...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 σελίδες
...(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 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 248 σελίδες
...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 σελίδες
...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. 
