 | Euclid - 1835 - 513 σελίδες
...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. e 47. 1. Upon AB describe » the square ABDC ; bisect5 AC in E, Book ir. and join BE ; produce CA to... | |
 | Robert Simson - 1835 - 513 σελίδες
...square of the other part. Let AB be the given straight Hue; it is required to divide it into two part", so that the rectangle contained by the whole, and...parts, shall be equal to the square of the other part. c 3. ']. ' e 47. 1. Upon AB describe * the square ABDC ; bisect b AC in E, Book II and join BE ; produce... | |
 | John Playfair - 1836 - 114 σελίδες
...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 (16. 2.) the square ABDC; bisect (8. 1.) AC in E, and join BE ; produce CA to F, and... | |
 | Euclides - 1837 - 88 σελίδες
...EF! + FG", and 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...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 - 1837 - 390 σελίδες
...(II. 9.) HB2 + 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 - 1837 - 240 σελίδες
...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
...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. From the point A draw* AC perpendicular and *" o™4 3' equal to AB ; bisect* AC in E, and join B,... | |
 | Euclid, Robert Simson - 1838 - 416 σελίδες
...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 - 1840 - 605 σελίδες
...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 - 1841 - 351 σελίδες
...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* the square ABDC; bisect* AC * 46. 1. in E, and join BE; produce CA to F, making*... | |
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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. 
