 | University of Oxford - 1863 - 316 σελίδες
...the rectangle contained by the whole and that part, together with the square of the other part. 9. If a straight line be bisected and produced to any point, the square of the whole line thus produced and the square of the part of it produced are together double... | |
 | Euclides - 1864 - 448 σελίδες
...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... | |
 | Euclides - 1864 - 262 σελίδες
...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 - 1865 - 528 σελίδες
...be the line so divided in the points C and Dj (fig. Euc-. n. 5) shew that A IP = 4.CD'i 4.AD.DB. 9. If a straight line be bisected and produced to any point, the square on the whole line when thus produced, is equal to the square on the part produced and four times... | |
 | Euclides - 1865 - 402 σελίδες
...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 - 1855 - 350 σελίδες
...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... | |
 | General Medical Council (Great Britain) - 1866 - 496 σελίδες
...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 - 224 σελίδες
...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 - 1867 - 424 σελίδες
...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 - 1867 - 474 σελίδες
...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... | |
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Prove it. 6.If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced together with the -square on half the line bisected, is equal to the square on the straight line... 
