 | Euclides - 1862 - 140 pages
...be equal to it. (dem. 4.) Conclusion. — Therefore, the straight lines, &c. QED PROPOSITION 34.— THEOREM. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal bisects it, that is, divides it into two equal parts. (References— Prop. I. 26, 29; ax.... | |
 | Euclides - 1862 - 172 pages
...whole angle ACD; (ax. 2) and the angle BAC has been shown to be equal to the angle BDC ; therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diameter shall bisect it. For because AB is equal to CD; and BC common, the two AB, BC, are... | |
 | 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 straight line apply a parallelogram,... | |
 | Euclides - 1863 - 122 pages
...2) to the-whole angle ACD; and the angle BAC has been proved to be equal to the angle BDC. Therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diagonal Be bisects the parallelogram AD. Because in the two triangles ABC, DCB, AB is equal... | |
 | Euclides - 1864 - 262 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 of this proposition. Also shew that a quadrilateral... | |
 | Euclides - 1864 - 448 pages
...to the whole angle A CD ; (ax. 2.) and the angle BA C has 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,... | |
 | Euclides - 1865 - 402 pages
...whole angle ACD ; (ax. 2) and the angle BAC has been shown to be equal to the angle BDC ; therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diameter shall bisect it. For because AB is equal to CD, and BC common, the two AB, BC, are... | |
 | Robert Potts - 1865 - 528 pages
...to the whole angle ACD; (ax. 2.) and the angle BA C has been shewn to be equal to BD C ; 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,... | |
 | 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... | |
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And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax. 
