 | Euclides - 1821 - 294 pages
...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 - Geometry - 1837 - 410 pages
...through 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 pages
...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 - Geometry - 1841 - 378 pages
...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... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...the 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 pages
...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 pages
...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 - Education - 1847 - 624 pages
...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... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...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... | |
 | Great Britain. Council on Education - Education - 1848 - 596 pages
...[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... | |
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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. 
