| Robert Potts - 1864
...rectangle PF. PC may be equal to the rectangle PD. PA. 164. To produce a given straight line, so that **the rectangle contained by the whole line thus produced, and the part of it produced,** shall be equal to a given square. 165. Two straight lines stand at right angles to each other, one... | |
| Robert Potts - 1864
...rectangle PF.PCmay be equal to the rectangle PD.PA. 164. To produce a given straight line, so that **the rectangle contained by the whole line thus produced, and the part of it produced,** shall be equal to a given square. 165. Two straight lines stand at right angles to each other, one... | |
| Alexander Kennedy Isbister - 1865
...double of the square on half the line, and of the square on the intermediate part ......... 1.9. 4. **If a straight line be bisected and produced to any point, the** square on the whole line thus produced, and the square on the part of it produced, are together double... | |
| John Playfair, Euclid - Geometry - 1855 - 317 pages
...is equivalent *o tht difference of their squaret / E 7, Jl E & I PROP. VI THEOR. If a straight tine **be bisected, and produced to any point ; the rectangle...produced, and the part of it produced, together with** th» square of half the line bisected, is equal to the square of the straight line which is made up... | |
| w.j.golbourn - 1866
...parallelogram are equal to one another. 1. Add together c\vt. 17 it; 8 19 qrs. 8 2 3 1 11.9 21 20 6 8 3. If _ **straight line be bisected, and produced to any point,...by the whole line thus produced .and the part of it** produeed, together with the square of half the line bisected, is equal to the square of the straight... | |
| 1867
...shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 10. **If a straight line be bisected, and produced to any...the part of it produced, together with the square** on half the line bisected, is equal to the square on the straight line which is made up of the half... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...lines AC, CD, is equal to the rectangle contained by their sum and difference. PROPOSITION 6. THEOREM. **If a straight line be bisected, and produced to any point, the rectangle** cjntained by the whole line thus produced, and the part of it produced, together with the tquare on... | |
| Gerardus Beekman Docharty - Geometry - 1867 - 283 pages
...another problem of the same nature, in which it is required to p^gduce a straight line AB, such that **the rectangle contained by the whole line thus produced and the part** produced shall be equivalent to the square of the line AB itself. Bisect AB in C ; draw the perpendicular... | |
| Joseph Wolstenholme - Mathematics - 1867 - 344 pages
...extreme and mean ratio and produced so that the part produced is equal to the smaller of the segments, **the rectangle contained by the whole line thus produced and the part** produced together with the square on the given line, will be equal to four times the square ou the... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...are double of the squares on AC, CD. Wherefore, if a straight line &c, QED PROPOSITION 10. THEOREM. **If a straight, line be bisected, and produced to any point, the** square on the whole line thus produced, and the square on the part of it produced, are together double... | |
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