 | Mathematics - 1865 - 132 pages
...geometrically, in the following form, which is analogous to that of Euclid II. 5. If a circular arc be divided into two equal and also into two unequal parts, the rectangle contained by the chords of the two unequal arcs, together with the square on the chord of... | |
 | 1865 - 128 pages
...geometrically, in the following form, which is analogous to that of Euclid II. 5. If a circular arc be divided into two equal and also into two unequal parts, the rectangle contained by the chords of the two unequal arcs, together with the square on the chord of... | |
 | 1867 - 224 pages
...to three given straight lines, but any two whatever of these must be greater than the third. 5. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...the line made of AB and BC together. Wherefore, if a straight line &c. QED PROPOSITION 9. THEOREM. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are t 'gather double of the square on half the line and of the square on the... | |
 | James Maurice Wilson - Geometry - 1868 - 132 pages
...difference of any two lines is equivalent to the difference of the squares on those lines 61 THEOREM 28. If a straight line be divided into two equal and also...parts are together double of the square of half the Hue bisected, and the square on the line made up of the half and the part produced ........ 62 THEOREM... | |
 | Robert Potts - 1868 - 434 pages
...squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D. Then the squares on AD, DB together, shall... | |
 | James Maurice Wilson - 1869 - 260 pages
...theorems may be used to demonstrate other properties of divided lines. For example, THEOREM 28. If a straight line be divided into two equal and also into two unequal segments, the squares of the two unequal segments are together double of the square of half the line... | |
 | Cambridge univ, exam. papers - 1870 - 272 pages
...two equal parts. If the diagonals of a quadrilateral bisect one another, it is a parallelogram. 2. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the... | |
 | Euclides - 1870 - 270 pages
...the extraction of the Square root. PROP. 9. — THBOB. If a st. line be divided into two equal parts, and also into two •unequal parts, the squares of the two unequal parts are togetJier double of the square of the half line and of the square of the line between the points of... | |
 | Euclides - 1871 - 136 pages
...and sq. on AC =sum of the eight rectangles and XH =AEFD = sq. on AD. X X 0 K Tf -U -XZ~ F p -R 0 If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square an half the line and of the square on the... | |
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IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section. 
