 | 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... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...And it was shewn to be equal to it. Wherefore, the straight lines &c. QED PROPOSITION 3i. THEOREM. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects tJie parallelogram, that is, divides it into two equal parts. Note. A parallelogram... | |
 | 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... | |
 | John Gibson - 1881 - 64 pages
...be parallel to the base, prove that the triangle is isosceles. TEST PAPER E. Propositions 33-40. 1. The opposite sides and angles of a parallelogram are equal to one another. 2. Parallelograms on the same base and between the same parallels are equal to one another. 3. Triangles... | |
 | John Carroll (art master.) - Geometry - 1881 - 100 pages
...&c. :; HO LESSON XIX.— RECTILINEAL FIGURES INSCRIBED IN AND DESCRIBED ABOUT OTHERS— Continued. " The opposite sides (and angles) of a parallelogram are equal to one another." — Euclid i. 34. Problem 118. — Within any quadrilateral figure V WX Y to inscribe a parallelogram,... | |
 | 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... | |
 | 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... | |
 | Euclides - Euclid's Elements - 1881 - 236 pages
...equal to CD, and BC common to the two triangles ABC, DCB ; the two sides AB, BC, are equal c — 1. to the two DC, CB, each to each. And the angle ABC was proved to he equal to the angle BCD. Therefore the base AC is equal (I. 4) to the base BD, and... | |
 | John Carroll (art master.) - Geometry - 1881 - 100 pages
...Fig.lU. wzv LESSON XIX.— RECTILINEAL FIGURES INSCRIBED IN AND DESCRIBED ABOUT OTHERS— Continued. " The opposite sides (and angles) of a parallelogram are equal to one ,_ another." — Euclid i. 34. Problem 118. — Within any quadii'lateral figure VWXY to inscribe a... | |
 | Marianne Nops - 1882 - 278 pages
...shown 'to be equal to it. Wherefore the straight lines, &c. — QED PROPOSITION XXXIV., THEOREM 24. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects it. Let ACDB be a Ig*m. of which BC is a diameter. Then shall AB = DC, and... | |
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And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB... 
