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.
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Page 70
by Euclides - 1838

## The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...are double of the squares of AC, CD. Wherefore, if a straight line, etc. QED PROPOSITION XI. PROB. To divide a given straight line into two parts, so...parts, shall be equal to the square of the other part. Upon AB describe (46. i.) the square ABDC ; bisect (10. i.) AC in E, and join BE ; produce CA to F,...

## The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 pages
...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 rectangle contained by...parts shall be equal to the square of the other part. Upon ab describe (i. 46) the square abdС; bisect (i. 10) a С in e, and join be, produce С a to f,...

## The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...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 rectangle contained by...parts, shall be equal to the square of the other part. Upon AB describe (1. 46.) the square ABDC ; bisect (I. 10.) AC in E, and join BE; produce CA to F,...

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

Royal Military Academy, Woolwich - Mathematics - 1853 - 474 pages
...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 less part, and hence by the question we have x8 = 20 (20...

## The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...line. It is required to divide it into two such parts, that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. On AB describe (i. 46) the square ACDB ; and supposing A to be that extremity of AB adjacent to which...

## Solutions of the problems and riders proposed in the Senate-house ...

Cambridge univ, exam. papers - 1854 - 284 pages
...BD the other diameter, the difference of the parallelograms is equal to twice the triangle BKD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Produce a given straight...

## Solutions of the Problems and Riders Proposed in the Senate-house ...

William Walton, Charles Frederick Mackenzie - Education - 1854 - 266 pages
...BD the other diameter, the difference of the parallelograms is equal to twice the triangle BSD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Produce a given straight...

## Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 534 pages
...the remarks at the end of this book. PROPOSITION XI.— PROBLEM. To divide a given straight line (AB) into two parts, so that the rectangle contained by the whole, and от of the parts, shall be equal to the square of the other part. From A draw AC perpendicular and...