 | Gerardus Beekman Docharty - Geometry - 1867 - 474 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 - 368 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 - 426 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... | |
 | 1868 - 876 pages
...the right angle is equal to the squares described upon the sides which contain the right angle 20 4. If a straight line be bisected and produced to any...the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half... | |
 | Robert Potts - 1868 - 434 pages
...the rectangle contained by their sum AD and their difference DB. PROPOSITION VI. THEOREM. Tfaitraight line be bisected, and produced to any point; the rectangle contained by the whole line thus prodlwed, and the part of it produced, together with the square on half the line bisected, i3 equal... | |
 | Woolwich roy. military acad - 1868 - 426 pages
...the magnitudes of the angles of the different triangles referred to, complete the demonstration : " If a straight line be bisected and produced to any point, the squares of the whole line thus produced and the part of it produced are together double of the square... | |
 | Edinburgh univ - 1868 - 334 pages
...angles of a triangle can in no case exceed two right angles. 4. Give two proofs of Eucl. I. 47. 5. 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... | |
 | Robert Johnston (F.R.G.S.) - Civil service - 1869 - 196 pages
...shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 3. If a straight line be bisected, and produced to any...the part of it produced, together with the square of half the line bisected, is equal to the straight line which is made up of the half and the part... | |
 | Euclides - 1870 - 270 pages
...4 = 12 + 4 = 16 : extracting the square root, x + 2 = 4 /. x = 2. PROP. 6. — THEOR. If a st. tine be bisected and produced to any point, the rectangle...the part of it produced, together with the square of half the line bisected, is equal to the square of the st. line which is made up of the half and... | |
 | Euclides - 1871 - 136 pages
...in D, shew that the sum of the squares on AB, AC is equal to twice the sum of the squares on AD, BD. 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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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 of half the line bisected, is equal to the square of the straight line which is made... 
