 | Euclides - Euclid's Elements - 1837 - 112 pages
...that these = 2 AC* + 2 CD!. H PROPOSITION XI. E ._ Problem. To divide a given straight line into two parts, so that the rectangle contained by the whole...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... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...+ BD*, or AD2 + BD2= 5-a ' — 2CD2+2AC2.* PROP. XI. PROB. 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. Let AB be the given straight line ; it is required to... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...and of the mean distance. PROPOSITION XI. PROBLEM. To divide a given straight line in medial section. Let AB be the given straight line ; it is required to divide it in medial section. Upon AB describe the square ABDC (I. 46) ; bisect AC in E (1. 10), and join BE ;... | |
 | Euclides - 1838 - 264 pages
...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 the whole,...parts, shall be equal to the square of the other part. From the point A draw* AC perpendicular and *" o™4 3' equal to AB ; bisect* AC in E, and join B,... | |
 | Robert Simson - Geometry - 1838 - 434 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 intotwo equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the angle... | |
 | John D. Williams - Algebra - 1840 - 634 pages
...required to divide a line of 20 inches in length, into two such parts that the rectangle of the whple and one- of the parts shall be equal to the square of the other. Let one part — x ; then the other will be 20 — x. And by the question 20(20 — х)=з?, or ^+20^=400... | |
 | Euclides - Geometry - 1841 - 378 pages
...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 the whole...parts, shall be equal to the square of the other part. Upon AB describe* the square ABDC; bisect* AC * 46. 1. in E, and join BE; produce CA to F, making*... | |
 | Euclides - 1842 - 316 pages
...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 the whole, and one of the parts, shall be equivalent to the square of the other part. Upon AB describe (46. 1.) the square ABDC ; bisect (10.... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...is evident from this algebraical equality. PROP. XI. PROB. 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. Let AB be the given straight line ; it is required to... | |
 | Education - 1844 - 688 pages
...parts are together equal to the square of the whole line. 7. Divide a given straight line into two parts, so that the rectangle contained by the whole...parts shall be equal to the square of the other part. 8. If in a circle two straight lines cut one another, which do not both pass through the centre, they... | |
| |
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. 
