Books Books To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part. The Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 3-16
by Euclides - 1814 ## A Supplement to the Elements of Euclid

Daniel Cresswell - Euclid's Elements - 1825 - 616 pages
...whole tine and out; of Us parts, shall have a given ratio to the square of the other part *. Let Jli be the given straight line : It is required to divide it into two parts, such that the rectangle contained by AB and one of the parts shall have to the square of the other... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1826 - 326 pages
...reetangle eontained by the whole, and one of the parts, may be equal to the square of the other part. Let AB be the given straight line; it is required to divide it into two parts, so that the reetangle eontained by the whole, and one of tb.e parts, shall be equal to the square of the other... ## Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ...

Miles Bland - Euclid's Elements - 1827 - 462 pages
...whole line produced and the part produced may be equal to a given square. 9. To divide a straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square of a given line, which is less than the line to be divided. 10. To divide... ## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...PROP. X. PROB. To bisect a given Jinite straight line, that is, to divide it into two equal parts. Let AB be the given straight line ; it is required to divide it into two equal parts. Describe* upon it an equilateral triangle ABC, and * 1. 1. bisect* the angle ACB by the... ## Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...X. PROBLEM. To bisect a given finite straight line; that is, to divide it into two equal parts. Let AB be the given straight line; it is required to divide it into two equal parts. On AB describe an equilateral triangle ABC (1. 1.), and bisect the angle ACB by the straight... ## Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 358 pages
...rectangle contained by the whole, and one of the parts, may be equal to the square of the other part. Let AB be the given straight line; it is required to divide...that the rectangle contained by the whole, and one of the_parts, sha'l be equal to the square of the other part. Upon AB describe (40. 1.) the square ABDC;... ## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...PROP. X. PROB. To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line ; it is required to divide it into two equal parts. al. 1. Describe a upon it an equilateral triangle ABC, and bisect b9. i. bthe angle ACB... ## The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...rectangle con tained by the whole and one of the parts shall be equal to the square of the other part. Let AB be the given straight line : it is required to...parts shall be equal to the square of the other part. Upon AB describe (16. 2.) the square ABDC; bisect (8. 1.) AC in E, and join BE ; produce CA to F, and... ## Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - Mathematics - 1836 - 524 pages
...are now in a condition for showing how the same result may be arrived at geometrically. Let AB be any line, it is required to divide it into two parts, so that the square of one part shall be equal to the rectangle of the whole and the other part. At the point B,... 