 | Euclides - 1853 - 176 pagina’s
...triangle abc ^ equal to the triangle dbc. Wherefore triangles, &c. QED PROPOSITION XXXVIII. — THEOREM. Triangles upon equal bases, and between the same parallels, are equal to one another. LET the triangles a bc, def be upon equal bases bc, ef, and between the same parallels bf,... | |
 | Royal Military Academy, Woolwich - 1853 - 400 pagina’s
...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,... | |
 | Euclides - 1853 - 146 pagina’s
...triangle ABC is equal to the triangle DBC. Wherefore, triangles, &c. QED PROP. XXXVIII. — THEOREM. 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,... | |
 | Thomas Lund - 1854 - 520 pagina’s
...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... | |
 | Euclides - 1855 - 270 pagina’s
...thousand sides, he could reduce it, by degrees, to an equivalent triangle. PROP. XXXVIII. THEOREM. Triangles upon equal bases, and 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... | |
 | Euclides - 1856 - 168 pagina’s
...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... | |
 | Cambridge univ, exam. papers - 1856 - 200 pagina’s
...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... | |
 | 1857 - 486 pagina’s
...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... | |
 | Euclides - 1858 - 248 pagina’s
...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... | |
 | Euclides - 1860 - 288 pagina’s
...(Ax. 7) ; therefore the triangle ABC is equal to the triangle DBC. . - . PROPOSITION XXXVUI. THEOREM. Triangles upon equal bases, and between the same parallels, are equal to one another. Given the triangles ABC and DEF upon equal bases BC and EF, and between the same parallels... | |
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Triangles upon equal bases, and between the same parallels, are equal to one another. 
