Books Books 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. An Elementary Treatise on the Geometrical and Algebraical Investigation of ... - Page 85
by Daniel Cresswell - 1817 - 436 pages ## A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 410 pages
...(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... ## A Supplement to the Elements of Euclid

Daniel Cresswell - Euclid's Elements - 1825 - 582 pages
...(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... ## Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 208 pages
...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... ## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 390 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.... ## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 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

...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... ## Arithmetic, algebra, differential and integral calculus, by W. Rutherford ...

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... ## The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...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.... ## Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

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... 