 | 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... | |
 | 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... | |
 | 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... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 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 AD* be a parallelogram, of which BC is a diagonal ; (1) the... | |
 | 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... | |
 | 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... | |
 | Euclides - 1852 - 48 pages
...alternate angles, therefore the lines A c and в D are parallel (Prop. 27.). WWD PKOP. XXXIV. THEOB. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal divides it into two equal parts. Let AB c D be a parallelogram, and B c the diagonal... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...; and it was shown to be equal to it. Therefore straight lines, etc. QED PROPOSITION XXXIV. TUEOR. The opposite sides and angles of a parallelogram are equal to one an.other, and the diameter bisects it, that is, divides it into two equal parts. NB A parallelogram is a four-sided... | |
 | Popular educator - 1854 - 922 pages
...whole angle A c D ; and the angle ВАС has been proved to be equal to the angle в D с ; therefore the opposite sides and angles of a parallelogram are equal to one another. Abo the diagonal в с bisects the parallelogram A D. Because in the two triangles ABC and D с в,... | |
 | Euclides - 1855 - 270 pages
...the diagonal is the straight line joining the vertices of two opposite angles. PROP. XXXIV. THEOREM. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal bisects it, that is, divides it into UEO equal parts. Let AD be a parallelogram, of... | |
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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 the opposite sides are parallel : and the diameter... 
