 | Euclides - 1821 - 294 σελίδες
...parallelograms formed of which the given triangles as halves they are .-. equal, PROP. 39, THEOR. Equal triangles on the same base and on the same side of it are between the same parallels, For if they are not, draw through the vertex of one of them a line... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...a point in which the circumferences meet, the circles must touch one another in that point. IF two triangles on the same base, and on the same side of it, have equal vertical angles, the vertex of each is in the circumference of the circle described about... | |
 | Euclides - 1840 - 192 σελίδες
...therefore be also greater than Z. BDC, of which however it is but a part ; which is absurd. Therefore, two triangles on the same base, and on the same side of it, cannot have their conterminous sides equal at both extremities of the base, when the vertex of the... | |
 | Euclides - 1841 - 378 σελίδες
...therefore* the 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... | |
 | Euclides, James Thomson - 1845 - 382 σελίδες
...circumferences meet, the circles must touch one another in that point. PROP. III. THEOR. — If two triangles on the same base, and on the same side of it, have equal vertical angles, the vertex of each is in the circumference of the circle described about... | |
 | Euclides - 1845 - 546 σελίδες
...the 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... | |
 | Scottish school-book assoc - 1845 - 444 σελίδες
...PLANE 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... | |
 | Great Britain. Committee on Education - 1847 - 624 σελίδες
...to two 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... | |
 | Great Britain. Council on Education - 1848 - 596 σελίδες
...[J8472. 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... | |
 | J. Goodall, W. Hammond - 1848 - 390 σελίδες
...parallel 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... | |
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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. 
