| 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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