 | University of Oxford - Education, Higher - 1863 - 316 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 a« the iiimcers, mu»l 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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And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB... 
