 | 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... | |
 | 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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 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...together double of the square on half the line and of the squareon the line between thepoints of section. Let the straight line AB be divided into two equal... | |
 | 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... | |
 | Euclides - 1871 - 136 pages
...BC 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...two unequal parts are together double of the square an half the line and of the square on the line between the points of section. Let AB be divided equally... | |
 | Edinburgh univ - 1871 - 392 pages
...has the greater 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... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...on the hypotenuse is equal to the sum of the squares on the other two sides. (I. 47.) 2. That if a line be divided into two equal, and also into two unequal parts, the rectangle contained by the unequal parts together with the square on the part between the points of... | |
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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. 
