| John Playfair - Euclid's Elements - 1836 - 488 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...its diameter bisects it ; for AB being equal to CD,** arid BC common, the two AB, BC are equal to the two DC, CB, each to each ; now tfee angle ABC is equal... | |
| Mathematics - 1836 - 472 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... | |
| John Playfair - Geometry - 1837 - 332 pages
...ABD is equal to the whole angle ACD : And the angle BAG has been shewn to be equal to the angle BDC : **therefore the opposite sides and angles of a parallelogram...and BC common, the two AB, BC are equal to the two** IDC, CB, each to each ; now the angle ABC is equal to the angle BCD ; therefore the triangle ABC is... | |
| Euclid - 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... | |
| 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 - 1841 - 378 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,** Because AB is parallel to CD, AB BC are equal to the two DC, CB, each to each; and the angle ABC has... | |
| John Playfair - Euclid's Elements - 1842 - 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, divid'es it into two equal parts. NB A Parallelogram is a four-sided... | |
| Euclides - 1842 - 320 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... | |
| Euclid - Geometry - 1845 - 218 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,...DC, CB, each to each ; and the angle ABC is equal to** *. i. the angle BCD; therefore the triangle ABC is equal § to the triangle BCD, and the diameter BC... | |
| Euclides - 1845 - 544 pages
...ABD is equal 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 equal... | |
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