| 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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