| 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... | |
| 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... | |
| Euclides - 1865 - 402 pages
...in one straight line. Wherefore, if a straight line, &c. QED PROP. IX. — THEOREM. If a, straight **line be divided into two equal and also into two unequal parts;** then the squares of the two unequal parts are together double of the •quare of half the line, and... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...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... | |
| 1867 - 224 pages
...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... | |
| James Maurice Wilson - Geometry - 1868 - 132 pages
...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...the squares of the two unequal parts are together** double of the square of half the line bisected, and the square on the line made up of the half and... | |
| Cambridge univ, exam. papers - 1870 - 272 pages
...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
...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... | |
| Edinburgh univ - 1871 - 392 pages
...angle is greater than the base of the other. A complete demonstration is required. 4. If a straight **line be divided into two equal, and also into two unequal parts, the** rectangle contained by the unequal parts, together with the square of the line between the points of... | |
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