 | Euclides - 1855 - 270 sider
...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 BF, 'A D. The triangle... | |
 | Great Britain. Committee on Education - 1855 - 976 sider
...equal, each to each, namely, those to which the equal sides are opposite, 2. Parallelograms on the same base and between the same parallels are equal to one another. 3. In any triangle, if the square of one of the sides is equal to the squares of the two other sides,... | |
 | Euclides - 1856 - 168 sider
...to the parallelogram EHGF ; wherefore EHGF is also equal to ABC D. XXXIX.— EUCLID I. 37. Triangles upon the same base and between the same parallels are equal to one another. Let the triangles ABC, DBC (Fig. 31) be upon the same base BC, and between the same parallels AD, BC ; the... | |
 | Cambridge univ, exam. papers - 1856 - 252 sider
...Emmanuel College. WILLIAM HENRY BESAHT, MA St John's College. TUESDAY, January 6, 1857. 9... 12. 1. PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another. ABC is an isosceles triangle, of which A is the vertex : AB, AC, are bisected in D and E respectively... | |
 | William Pease - 1856 - 108 sider
...opposite the base, to meet these perpendiculars, and the required rectangle will be formed. REASON : " Parallelograms, upon the same base, and between the same parallels," are equal to each other. (Euclid, Book I. Prop. 35.) PROBLEM LXX. To make a rectangle, one of its sides being given,... | |
 | 1856 - 376 sider
...angles at the other side of the base are equal. ce, te anges at te oter se of te base are equa. 2. Parallelograms upon the same base and between the same parallels are equal. 3. To a given straight line to apply a parallelogram which shall be equal to a given triangle, ve one... | |
 | W F. Richards - 1856 - 198 sider
...are equal, and if the equal sides be produced, the angles at the other side of the base are equal. 2. Parallelograms upon the same base and between the same parallels are equal. 3. To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and... | |
 | War office - 1858 - 578 sider
...triangle be produced, the exterior angle is greater than either of the interior opposite angles. 2. Parallelograms upon the same base and between the same parallels are equal to one another. VOLUNTARY PORTION. 1. The opposite angles of a quadrilateral figure, inscribed in a circle, are together... | |
 | Euclides - 1868 - 88 sider
...5 Def. A. 6 D. 5. H. 7 P. 35. 8 P. 85. 9 Ax. 1. 10 Becap. • PilOP. XXXVII. Тикоа. Triangles upon the same base and between the same parallels are equal to one ano CON. Pst. 2. P. 31. Def. A. DEM. P. 35. 34. Ax. 7. SCHOL. PIIOP. XXXVIII. TIIEOU. Triangles upon... | |
 | Euclides - 1858 - 248 sider
...four-sided figures of which the opposite sides are parallel ; . . BGHA & BPKD are parallelograms. ix. Parallelograms upon the same base and between the same parallels, are equal : x. EBAF and BGHA are parallelograms on the same base, &c. ; .'. EBAF and BGHA are equal parallelograms.... | |
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PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another... 
