 | Euclides - 1841 - 378 σελίδες
...triangle BDE is* 9. 5. equal to the triangle CDE: and they are on the same base DE; but equal triangles on the same base, and on the same side of it, are between the same parallels ;* * 39. i therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROP. III. THEOR.... | |
 | Scottish school-book assoc - 1845 - 444 σελίδες
...GEOMETRY. other lino passing through A, except AD, which therefore is || to BF. QED Cor. 1. Equal triangles on the same base and on the same side of it, are between the same parallels. Cor. 2. In the same manner it might be shown that equal triangles between the same parallels are upon... | |
 | Euclides - 1845 - 546 σελίδες
...triangle BDE is equal to the triangle CDE : (v. 9.) and they are on the same base DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i. 39-) therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROPOSITION III.... | |
 | Euclides - 1846 - 272 σελίδες
...Prop. 34), and therefore are also equal (by Ax. 7.) PROPOSITION XXXIX. THEOREM. Equal triangles (BAC and BDC) on the same base, and on the same side of it, are between the same parallels. For if AD be not parallel to BC, draw through the point A the right line AF parallel to BC, cutting the side... | |
 | Euclides - 1846 - 292 σελίδες
...triangles upon S,c, QED PROP. XL. THEOR. Equal triangles upon equal bases, in the same straight line, and on the same side of it, are between the same parallels. Let the equal triangles, ABC, DEF, be upon equal bases BC, EF, in the same straight line BF, and on... | |
 | Great Britain. Committee on Education - 1847 - 624 σελίδες
...right angles, these two straight lines shall be in one and the same straight line. 3. Equal triangles on the same base and on the same side of it are between the same parallels. Section II. 1. In a given straight line find a point equally distant from two given points, one in... | |
 | Great Britain. Council on Education - 1848 - 596 σελίδες
...Right lines which are parallel to the same right line are parallel to one another. 3. Equal triangles on the same base, and on the same side of it, are between the same parallels. Section 5. 1. If a right line be divided into any two parts, the squares of the whole line and one... | |
 | J. Goodall, W. Hammond - 1848 - 390 σελίδες
...to one another. 1. The greater side of every triangle subtends the greater angle. 3. Equal triangles on the same base and on the same side of it, are between the same parallels. Section 5. 1. If a right line be divided into any two parts, the squares of the whole line and one... | |
 | Great Britain. Committee on Education - 1848 - 606 σελίδες
...lines which are parallel lo the same right line are parallel to one another. 3. Equal triangles or» the same base, and on the same side of it, are between the same parallels. Section 5. 1. If a right line be divided into any two parls, the squr.res of the whole line and one... | |
 | Great Britain. Committee on Education - 1855 - 976 σελίδες
...fails when this precaution is not taken, and give a proof in this case. Section 2. 1. Equal triangles on the same base, and on the same side of it, are between the same parallels. 2. If the square described upon one of the sides of a triangle be equal to the squares described upon... | |
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DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i. 
