 | 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 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... | |
 | 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... | |
 | 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... | |
 | 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 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... | |
 | 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... | |
 | 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 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... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...enunciation. Prop. VIII. is usually passed over, as it is troublesome iinil useless. PBOPOSITION IX. If a straight line be divided into two equal and also into two unequal parts, the squares on the two unequal parts are together equal to twice the square on half the line together... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...of the eight rectangles and XH =AEFD — sq. on AD. QED JC G ^ V 0 JT j> it PROPOSITION IX. THEOREM. 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... | |
 | Henry Major - Student teachers - 1873 - 588 pages
...rectangle AC, CB. Coa. The parallelograms about the diameter of it square, are likewise squares. ,7\ V. — 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... | |
| |
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. 
