 | Mathematics - 1836 - 488 pages
...and parallel straight lines, towards the same parts, are also themselves equal and parallel. XXXIV. The opposite sides and angles of a parallelogram are...equal to one another, and the diameter bisects it, that is, divides it into two equal parts. XXXV. Parallelograms upon the same base and between the same... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...to two right angles ; therefore, the opposite sides must be equal and parallel. PROP. XXXIV. THEOR. 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. NB A Parallelogram is a four-sided... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...quadrilateral which has two sides equal and parallel, is (I. def. 24.) a parallelogram. PROP. XXXIV. THEOR. THE opposite sides and angles of a parallelogram are equal to one another ; and (2.) the diagonal bisects it. Let ADf be a parallelogram, of which BC is a diagonal; (1.) the opposite... | |
 | Euclides - 1838 - 264 pages
...to BD : and it was shown to be equal to it. Therefore, straight lines, &c. QED PROP. XXXIV. THEOR. The opposite sides and angles of a parallelogram are...equal to one another, and the diameter bisects it, that is, divides it into two equal parts. N. B — A parallelogram is a four-sided figure, of which... | |
 | Euclides - 1842 - 316 pages
...to BD ; and it was shown to be equal to it. Therefore, straight lines, &c. QED PROP. XXXIV. THEOR. THE opposite sides and angles of a parallelogram are equal to one another, and the diameter, or diagonal, bisects the figure. NB A parallelogram is a four-sided figure, of which the opposite sides... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...to the whole angle ACD : And the angle BAC has been shewn to be equal to the angle BDC : therefore the opposite sides and angles of a parallelogram are equal to one another ; also, its diameter bisects it ; for AB being equal to CD, and BC common, the two AB, BC are equal... | |
 | Euclides - 1845 - 546 pages
...to the whole angle ACD • (ax. 2.) and the angle BAC 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 are... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...ABD is equal (I. ax. 2) to the whole angle ACD; and BAC has been shown to be equal to BDC : therefore the opposite sides and angles of a parallelogram are equal to one another. Also (I. 26, part 3) the triangle ABC is equal to the triangle DCB ; that is, the diagonal BC bisects... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...is four right angles ; of a pentagon, six right angles; of a hexagon, eight, &c. PROPOSITION XXIX. THEOREM. The opposite sides and angles of a parallelogram are equal to each other. Let ABDC be a parallelogram; then will its opposite sides and angles be equal to each other.... | |
 | Great Britain. Committee on Education - School buildings - 1850 - 790 pages
...breadth by 16 yards, and it contains 960 yards ; find the length and breadth. GEOMETRY. Section 1. 1. The opposite sides and angles of a parallelogram are...equal to one another, and the diameter bisects it, that is, divides it into two equal parts. 2. The angle at the centre of a circle is double of the angle... | |
| |
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. 
