| University of Oxford - Education, Higher - 1863 - 328 pages
...rectangle contained by the whole and one of the parts may be equal to the square on the other part. 4. **The opposite sides and angles of a parallelogram are equal to one another,** and the diameter bisects the parallelogram, that is, divides it into two equal parts. 5. To a given... | |
| Euclides - 1864 - 262 pages
...another. Also the diameter BC bisects it. For since AB is equal to CD, and BC common, the two sides **AB, BC, are equal to the two DC, CB, each to each, and the** ansle ABC has been proved to be equal to the angle BCD ; therefore the triangle ABCis equal to the... | |
| Euclides - 1864 - 448 pages
...as well as those which bisect any two interior angles of a parallelogram, contain a right angle. 78. **The opposite sides and angles of a parallelogram are equal to one another,** and the diameters bisect it. State and prove the converse iposition. Also shew that a quadrilateral... | |
| Euclides - 1865 - 402 pages
...same straight line, they are parallel to each other . . . . . I. 30. E. Relating to Parallelograms. 1. **The opposite sides and angles of a parallelogram are equal to one another,** and the diameter that bisects it, that is, divides it into two equal parts. . . . . . . . I. 34. 2.... | |
| Robert Potts - 1865 - 528 pages
...as well as those which bisect any two interior angles of a parallelogram, contain a right angle. 83. **The opposite sides and angles of a parallelogram are equal to one another,** and the diameters bisect it. State and prove the converse of this proposition. Also shew that a quadrilateral... | |
| William Harris JOHNSTON - 1865 - 478 pages
...generally, quadrilateral*. A quadrilateral formed by two pairs of parallel sides is called a parallelogram. **The opposite sides and angles of a parallelogram are equal to one another.** (Euclid, Book I., Prop. 34.) When the sides of a parallelogram are joined at right angles, or are perpendicular... | |
| General Medical Council (Great Britain) - 1866 - 496 pages
...of question*, at well aĞ the iiimcers, muğl be exhibited. ELEMENTS OF MATHEMATICS AND ALGEBRA 1. **The opposite sides and angles of a parallelogram are equal to one another.** 4. A rifle-ball is discharged horizontally from a position 1000 feet above the level of the sea. What... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...And it was shewn to be equal to it. Wherefore, the straight lines &c. QED PROPOSITION 34. THEOREM. **The opposite sides and angles of a parallelogram are equal to one another,** and the diameter bisects the parallelogram, that is, divides it into two equal parts. Note. A parallelogram... | |
| Robert Potts - 1868 - 434 pages
...ABD is equal to the whole angle A CD ; (ax. 2.) and the angle B-^Chas been shewn to be equal to BDC; **therefore the opposite sides and angles of a parallelogram are equal to one another. Also** the diameter BC bisects it. For since AB is equal to CD, and BC common, the two sides AB, BC, are equal... | |
| General Medical Council (Great Britain) - 1869 - 402 pages
...triangle be produced the exterior angle is greater than either of the interior opposite angles. 4. **The opposite sides and angles of a parallelogram are equal to one another,** and the diagonal bisects it. 5. To divide a straight line into two parts so that the rectangle contained... | |
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