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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.
Elements of geometry, based on Euclid, books i-iii - Page 71
by Edward Atkins - 1876 - 119 pages

## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...AD, DB are double the squares of AC, CD. Wherefore, " if a straight line," &c. QED PROP. XI. PROB. To divide a given straight line into two parts, so...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 divide it into two parts, so...

## The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 513 pages
...CD. Wherefore, " if a straiglit line," &.c. QED PROP. XI. PROB. To divide a given straight line info two parts, so that the rectangle contained by the...and one of the parts, shall be equal to the square of the other part. Let AB be the given straight Hue; it is required to divide it into two part", so...

## The Element of Geometry

John Playfair - Geometry - 1836 - 114 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...and one of the 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 ;...

## A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...AG"; and that this = AC* + CE* + EF! + FG", and that these = 2 AC* + 2 CD!. H PROPOSITION XI. E ._ Problem. To divide a given straight line into two...and one of the parts shall be equal to the square of c KT~i the other part. Steps of the Demonstration. 1. Prove that CF x FA + AE* = EF*, and that this...

## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...HB, AD are equal. Then c B (II. 9.) HB2 + BD*, or AD2 + BD2= 5-a ' — 2CD2+2AC2.* PROP. XI. PROB. To divide a given straight line into two parts, so...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...

## Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...AD, DB are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROS. To divide a given straight line into two parts, so...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 divide it into two parts, so...

## The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 pages
...AD, DB are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROB. 1 To divide a given straight line into two parts, so...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 divide it into two parts, so...

## Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 320 pages
...are equivalent to double the squares of AC, CD. If therefore a straight line, &c. QED PROP. XI. PROB. To divide a given straight line into two parts, so...contained by the whole, and one of the parts, shall be equivalent to the square of the other part. Let AB be the given straight line : it is required to divide...

## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...(2a-f*)2+*2=2a2+2(a+i)2, and the proposition is evident from this algebraical equality. PROP. XI. PROB. To divide a given straight line into two parts, so...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...

## Proceedings

Scotland free church, gen. assembly - 1847 - 552 pages
...the squares described on the other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. 4. The angle in a semicircle...