 | Daniel Cresswell - 1817 - 454 páginas
...four sides all equally distant from the four sides of the given rectangle. (XXVII.) To divide a given straight line into two parts, such, that the rectangle contained by the whole line and one of its parts, shall have a given ratio to the square of the other part. (XXVIII.) The base, the vertical... | |
 | Daniel Cresswell - 1819 - 446 páginas
...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 line and one of its parts, shall have a given ratio to the square of the other part. Let AB be the given straight... | |
 | Miles Bland - 1819 - 444 páginas
...drawn from three given points shall make with each other angles equal to given angles. 6. To divide a straight line into two parts such that the rectangle contained by them may be equal to the square of their difference. 7. If a straight line be divided into any two... | |
 | Miles Bland - 1819 - 442 páginas
...AE, BE. Then the angle AEC=ABD, and AEB is of the given magnitude, by construction. (6.) To divide a straight line into two parts such, that the rectangle contained by them may lie equal to the square of their difference. Let AB be the given line ; upon it describe a... | |
 | Daniel Cresswell - 1825 - 616 páginas
...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... | |
 | Euclid, James Thomson - 1837 - 410 páginas
...particular case of this problem in which the given lines are equal. PROP. XXIII. PROB. To divide a given straight line into two parts, such. that the rectangle contained by the whole and one of the parts may have a given ratio to the square of the other. Let AB (see the last figure)... | |
 | Euclid, James Thomson - 1845 - 382 páginas
...particular case of this problem m which the given lines are equal. PROP. XXIII. PROR. — To divide a given straight line into two parts, such that the rectangle contained by the whole and one of the parts may have a given ratio to the square of the other. Let AB (see the last figure)... | |
 | Euclides - 1845 - 546 páginas
...of the squares of the two parts shall be equal to twice the rectangle contained by them. 4. Divide a straight line into two parts such, that the rectangle contained by them may be equal to the square of their difference. 5. To divide a straight line so that the rectangle... | |
 | Euclid, Robert Potts - 1847 - 118 páginas
...and .-. BH2 = AH2 - AH . BH = AH . (AH - BH) ; or, HD2 = AH . AD ; that is, AH is divided in D, so that the rectangle contained by the whole line and one part, is equal to the squi-re of the other part. By a similar process, HD may be so divided; and so on, by always taking... | |
 | University of Durham - 1851 - 222 páginas
...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... | |
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HL' : that is, AH is divided in L, so that the rectangle contained by the whole line AH and one part, is equal to the square on the other part HL. 
