 | 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 line, &c. QED PROP. III. THEOR.... | |
 | Scottish school-book assoc - 1845 - 444 pages
...any 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 the same parallels are upon... | |
 | Euclides - 1845 - 546 pages
...therefore 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 line, &c. QED PROPOSITION III.... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...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 - 1846 - 272 pages
...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 pages
...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 - Education - 1847 - 624 pages
...equal 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 from two given points, one in... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...line are 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 of the whole line and one... | |
 | Great Britain. Council on Education - Education - 1848 - 596 pages
...College [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 of the whole line and one... | |
 | Great Britain. Committee on Education - 1848 - 606 pages
...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... | |
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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. 
