 | Euclid, James Thomson - Geometry - 1845 - 380 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... | |
 | John Playfair - Euclid's Elements - 1846 - 332 pages
...ABD is equal 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...two AB, BC are equal to the two DC, CB, each to each ; now the angle ABC is equal to the angle BCD ; therefore the triangle ABC is equal (4. 1.) to the... | |
 | Euclides - 1846 - 292 pages
...opposite sides and angles of parallelograms are equal to one another : Also, the diameter bisects them ; for AB being equal to CD, and BC common, the two AB, BC arc equal to the two DC, CB, each to each, and the angle ABC is equal to the angle BCD — therefore... | |
 | John Playfair - Euclid's Elements - 1849 - 332 pages
...shewn to be equal to the angle BDC : therefore the opposite sides and angles of a parallelogramjare equal to one another ; also, its diameter bisects...and BC common, the two AB, BC are equal to the two ujfa CB, each to each ; now the angle ABC is equal tb the angle BCD ;-?&erefore the triangle ABC is... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...angle ABD is equal to the whole angle ACD. But the angle BAC has been proved equal to the angle BDC; therefore the opposite sides and angles of a parallelogram are equal to each other. PROPOSITION xxx. THEOKEM (Converse of Prop. XXIX.). If the opposite sides of a quadrilateral... | |
 | 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... | |
 | Euclides - 1853 - 146 pages
...opposite sides and angles of parallelograms are equal to one another. Also, their diameter bisects them ; for AB being equal to CD, and BC common, the two AB,...to the two DC, CB, each to each ; and the angle ABC has been proved equal to the angle BCD; therefore (I. 4.) 5. The triangle ABC is equal to the triangle... | |
 | 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 - 940 pages
...to the 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,... | |
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And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB... 
