| Euclides - 1865 - 402 pages
...added together 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... | |
| Robert Potts - 1865 - 528 pages
...the diameters of the squares on its two sides. 17. If a straight line be divided into two equal and **into two unequal parts, the squares on the two unequal parts are** equal to twice the rectangle contained by the two unequal parts, together with four times the square... | |
| 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... | |
| 1867 - 224 pages
...equal 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...the 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.... | |
| 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...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 line between the points of... | |
| James Maurice Wilson - Geometry - 1868 - 132 pages
...three 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 parts, the squares** of the two unequal parts are together double of the square of half the line bisected, and the square... | |
| Robert Potts - 1868 - 434 pages
...the diameters of the squares on its two sides. 15. If a straight line be divided into two equal and **into two unequal parts, the squares on the two unequal parts are** equal to twice the rectangle contained by the two unequal parts, together with four times the square... | |
| James Maurice Wilson - 1869 - 260 pages
...lines is equivalent to the difference of the squares tin those lines 6l One Corollary. 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...the 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.... | |
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