| John Playfair - Geometry - 1855 - 318 pages
...contain" ed by their sum and difference, or that AC 2 — CD 2 =(AC+CD) (AC — SCHOLIUM. PROP. VI THEOR. **If a straight line be bisected, and produced to any point; the rectangle** contamed by the whole line thus produced, and the part of it produced, together with the square of... | |
| Cambridge univ, exam. papers - 1856
...on the other two sides of it; the angle contained by these two sides is a right angle. 5. If a right **line be bisected, and produced to any point ; the...half the line bisected, is equal to the square of the** right line which is made up of the half and the part produced. Prove this proposition algebraically.... | |
| John Playfair - Euclid's Elements - 1856 - 318 pages
...of two quantities, is equivalent to the difference of their squares / £ / It E Cr I PROP. VI THEOR. **If a straight line be bisected, and produced to any...the square of half the line bisected, is equal to** t/u; square of the straight line which is made up of the half and the part produced. Let the straight... | |
| Euclides - 1856
...straight lines, and the other their difference, is equal to twice the squares of the same lines. LIV. * **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... | |
| George Moody - 1857
...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... | |
| Euclides - 1858
...then z2 +4z+4= 12 + 4= 16 ; extracting the square root, z + 2=4 .-.x =2. PROP. 6. — THEOR. If a st. **line be bisected and produced to any point, the rectangle...half the line bisected, is equal to the square of the** st. line which is made up of the half and the part produced. CONS.— 46. I., Pst. 1, and 31. I. DBM.—... | |
| Great Britain. Civil Service Commission - 1858
...6. The quadrilateral figuro whose diameters bisect each other is a parallelogram. BOOK II. 7. PROP. **VI. — If a straight line be bisected and produced...thus produced, and the part of it produced, together** witli the square of half the line bisected, is equal to the square of the straight line which is made... | |
| War office - 1858 - 12 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
...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... | |
| Sandhurst roy. military coll - 1859 - 1869 pages
...arrangement.] 1. To bisect a given finite straight line, that is, to divide it into two equal parts. 3. **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... | |
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