 | Thomas Lund - 1854 - 520 σελίδες
...things must themselves be equal; .'. the triangle BCD = the triangle FGH ' that is, all triangles upon the same, or equal bases, and ' between the same parallels', are equal to one another. * ' Parallelogram ' being a long word, when it occurs frequently, it is allowable to abridge it thus,... | |
 | Euclides - 1855 - 270 σελίδες
...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 BF, 'A D.... | |
 | Cambridge univ, exam. papers - 1856 - 200 σελίδες
...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... | |
 | Euclides - 1856 - 168 σελίδες
...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,... | |
 | 1857 - 486 σελίδες
...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 σελίδες
...four-sided figure, of which the opposite sides are parallel. DEMONSTRATION. — P. 38. Triangles upon equal bases and between the same parallels are equal to one another. P. 41. If a parallelogram and a triangle be upon the same base and between the same parallels, the... | |
 | Sandhurst roy. military coll - 1859 - 672 σελίδες
...bisect a given rectilineal angle, that is, to divide it into two equal angles. 2. Parallelograms on equal bases, and between the same parallels, are equal to one another. 3. In obtuse-angled triangles if a perpendicular be drawn from either of the acute angles to the opposite... | |
 | Euclides - 1860 - 288 σελίδες
...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 BF, AD ;... | |
 | Robert Potts - 1860 - 380 σελίδες
...equal to the triangle DBC. Wherefore, triangles, &c. QED PROPOSITION XXXViII. THEOREM. T•iangles 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. Then... | |
 | Royal college of surgeons of England - 1860 - 332 σελίδες
...three interior angles of every triangle are together equal to two right angles. 5. 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 squares on the whole line and one of the parts... | |
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Triangles upon equal bases, and between the same parallels, are equal to one another. 
