 | Euclides - 1853 - 146 sider
...because the diameter DC bisects it. But the halves of equal things are equal (Ax. 7.) ; therefore 5. The triangle ABC is equal to the triangle DBC. Wherefore,...between the same parallels, are equal to one another, Let the triangles ABC, DEF, be upon equal bases BC, EF, and between the same parallels BF, AD. The... | |
 | Royal Military Academy, Woolwich - 1853 - 400 sider
...the half of the parallelogram DBCF, because the diameter DC bisects it : PROPOSITION XXXVIII. THEOR. Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon equal bases BC, EF, and between the same parallels BF, AD : the... | |
 | Euclides - 1853 - 176 sider
...Therefore parallelograms upon the same base, &c. QED PROPOSITION XXXVI. — THEOREM. Parallelograms upon equal bases, and between the same parallels, are equal to one anotJier. a de ЬЕТ abСd, efgh, be parallelograms upon equal bases bС, fg, and between the same... | |
 | Thomas Lund - 1854 - 520 sider
...is contained in AB, and BEFC into as many as the unit is contained in BE. Then since parallelograms upon equal bases and between the same parallels are equal to one another (41 Cor. 1), the smaller parallelograms which make up ABCD, and BEFC, are all equal. Therefore the... | |
 | Euclides - 1855 - 270 sider
...that, if a figure had a thousand sides, he could reduce it, by degrees, to an equivalent triangle. PROP. XXXVIII. THEOREM. Triangles upon equal bases,...between the same parallels, are equal to one another. Let the triangles ABС, DEF, he upon equal bases B С, EF, and between the same parallels BF, 'A D.... | |
 | Euclides - 1856 - 168 sider
...of the parallelogram DBCF (Prop. 37) ; wherefore the triangle ABC is equal to the triangle DEC. XL. Triangles upon equal bases and between the same parallels are equal to one another. Let the triangles ABC, DEF (Fig. 32) be upon equal bases BC, EF, and between the same parallels BF,... | |
 | Cambridge univ, exam. papers - 1856 - 200 sider
...alternate angles equal to each other, these two straight lines shall be parallel. 4. Parallelograms upon equal bases, and between the same parallels, are equal to one another. 6. If a straight line be divided into any two parts, the rectangle contained by the whole and one of... | |
 | 1857 - 486 sider
...on the same base AB, but on opposite sides of it; join CD, cutting AB in E: then shall CE = ED. 10. Triangles upon equal bases, and between the same parallels, are equal to one another. 11. In a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than... | |
 | Euclides - 1858 - 248 sider
...2. 1 Pst. 2. 2 P. 31. 3 Def. A. 1 C.3&H. 2 3 P. 35. P. 34. 4 5 Ax. 7. Recap. CTE PROP. 38.— THEOR. Triangles upon equal bases and between the same parallels, are equal to one another. CONSTRUCTION. — Pst. 2. A st. line may be produced indefinitely. P. 31. To draw a line through a... | |
 | Euclides - 1868 - 88 sider
...equal to one ano CON. Pst. 2. P. 31. Def. A. DEM. P. 35. 34. Ax. 7. SCHOL. PIIOP. XXXVIII. TIIEOU. Triangles upon equal bases and between the same parallels are equal to one anoti Coy. Pst. 2. P. 31. Def. A. DEM. P. 36. 34. Ax. 7. EXP. 1 Hyp. 1. ,, 2. 2 Concl. CON. 1 Pst.... | |
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Triangles upon equal bases, and between the same parallels, are equal to one another. 
