 | Moffatt and Paige - 1879 - 474 pages
...and AC was shown to be equal to B D. Therefore, the straight lines which join the extremities, etc. QED Proposition XXXIV. Theorem. The opposite sides...equal to one another, and the diameter bisects it, that is, divides it into two equal parts. Let ACDB be a parallelogram, of which BC is a diameter. Then... | |
 | Edward Harri Mathews - 1879 - 94 pages
...or -third sides equal. 2. Any two angles of a triangle are together less than two right angles. 3. The opposite sides and angles of a parallelogram are equal to one another. 4. If two isosceles triangles have the same base the line which joins their summits is at right angles... | |
 | 1880 - 594 pages
...farms, must have resembled the most flourishing parts of Lombardy or the Netherlands." Euclid. — i. 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. Two parallel lines cut a series of parallel lines ; show... | |
 | Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...each, namely those to which the equal sides are opposite. 8. The opposite sides as well as the opposite angles of a parallelogram are equal to one another, and the diameter bisects it. If the two diameters are drawn, show that they bisect each other, and that the parallelogram will be... | |
 | T S. Taylor - 1880 - 152 pages
...enunciations of Euc. I. 26 and I. 29; and Axiom 2, and the definition of a parallelogram. General Enunciation. The opposite sides and angles of a parallelogram are equal to one another. Particular Enunciation. Given. — The parallelogram AB CD. Required. — To prove that (a) AB is equal... | |
 | Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...bisecting AB and AC in D and F respectively is parallel to the base BC. PROP. XXXIV. THEOREM. Th/>, opposite sides and angles of a parallelogram are equal to one another, and tlie diameter bisects the parallelogram, that is, divides it into two equal parts. Let ABDC be a parallelogram,... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...whole angle A CD. [Ax. 2. And the angle BA C has been shewn to be equal to the angle CDB. Therefore the opposite sides and angles of a parallelogram are equal to one another. Also the diameter bisects the parallelogram. For AB being equal to CD, and BC common, the two sides... | |
 | Education, Higher - 1884 - 538 pages
...line drawn through the point of bisection to meet the two lines will be bisected in that point. 6. The opposite sides and angles of a parallelogram are equal to one another and the diagonal bisects it. If both diagonals be drawn they bisect each other. 8. If a straight line be divided... | |
 | Moffatt and Paige - 1881 - 176 pages
...sum of the angles of every figure is equal to an even number of right angles. 2. The opposite side and angles of a parallelogram are equal to one another, and the diameter bisects it, that is, divides it into two equal parts. 3. To describe a square upon a given straight line. ALGEBRA.... | |
 | John Gibson - 1881 - 302 pages
...straight lines FH, FK are less than the two sides GH, GK but contain a greater angle. 3. Prove that the opposite sides and angles of a parallelogram are equal to one another, and that the diameter bisects the parallelogram. 4. Prove that parallelograms upon the same base and between... | |
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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. 
