| Daniel Cresswell - Euclid's Elements - 1825 - 582 pages
...produced, shall be to the square of the part produced, in a given ratio. VIII. PR. To divide a given finite **straight line into two parts, so that the rectangle, contained by the whole** line, and the difference of those two parts, shall be in a given ratio to the square of the less of... | |
| Robert Simson - Trigonometry - 1827 - 513 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* the square ABDC; bisect* AC in E, ahd join BE : produce CA to F, and make* EF equal... | |
| Miles Bland - Geometry - 1827 - 377 pages
...contained by the 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... | |
| John Playfair - Euclid's Elements - 1832 - 333 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 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;... | |
| Euclid - 1835 - 513 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.** e 47. 1. Upon AB describe » the square ABDC ; bisect5 AC in E, Book ir. and join BE ; produce CA to... | |
| 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...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 - Euclid's Elements - 1837 - 88 pages
...= AC* + CE* + 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...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 - 390 pages
...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 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... | |
| 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,... | |
| John D. Williams - Algebra - 1840 - 605 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... | |
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