 | Education - 1857 - 1266 pages
...To a given straight line apply a rectangle equal to a given rectilineal figure. SECTION II. — 1. If a straight line be bisected and produced to any point, the squares of the whole une produced and the part of it produced arc together double of the squares of... | |
 | War office - 1858 - 578 pages
...following equations (1) f+f_£=l V ; a T3 4 2 (2) (#-5) (x-2) -(x-5) (2x-5) + (x+1) (sc-2) =0 Euclid. 1. If a straight line be bisected, and produced to any...rectangle contained by the whole line thus produced, together with the square of half the line bisected, is equal to the square of the straight line which... | |
 | Euclides - 1858 - 136 pages
...USE. l. PROP. V. Bootc IT. Pnot.. VI. THEOR. If u st. Um; be bisecti;d and produced to any poiiti, the rectangle contained by the whole line thus produced and the part of it produced, toyether with the square of half the line bisrcted, is equal la ihe square of the st. line which is... | |
 | John Playfair - Geometry - 1860 - 334 pages
...difference, or that AC 2 —CD 2 =(AC+CD) (AC— • : CD)." SCHOLIUM. PROP. VI THEOR. Ifastraightlinebe bisected, and produced to any point ; the rectangle contained by the whole line that produced, and the part of it produced, together with the square of half the tine bisected, is... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...of the squares on AC, CD. If therefore a straight line be divided, &c. QED PROPOSITION X. THEOREM. If a straight line be bisected, and produced to any point, the square en the whole line thus produced, and the square on the part of it produced, are together double... | |
 | EDUCATION SOCIETY'S PRESS, CULLA - 1860 - 612 pages
...line, so that the sum of the squares on the given line and the part produced may be equal to twice the rectangle contained by the whole line thus produced, and the part produced. 8 If a point be taken within a circle from which there fall more than two equal straight... | |
 | Euclides - 1862 - 140 pages
...squares on AC and CD. Conclusion. — Therefore, 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... | |
 | Robert Potts - 1863 - 482 pages
...side of the ground and back to the other post: determine the shortest course for him to pursue. 5. If a straight line be bisected and produced to any...rectangle contained by the whole line thus produced, ond the part of it produced, together with the square of half the line bisected, is equal to the square... | |
 | University of Oxford - Education, Higher - 1863 - 316 pages
...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 pages
...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... | |
| |
PROP. X. THEOR. 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 of the square of half the line bisected, and of the square of the line... 
