 | John Radford Young - Euclid's Elements - 1827 - 228 pages
...neither touch (Cor. 2.) nor cut. 4. It appears, therefore, that in order that two circumferences may cut, the distance of their centres must be less than...sum, and greater than the difference of the radii. PROPOSITION XIV. THEOREM. An inscribed angle is equal to an angle at the centre of the circle whose... | |
 | John Radford Young - Conic sections - 1830 - 360 pages
...must obviously subsist the conditions r + d -7 r', r + r' ~7d, r' + d 7 r, which prove that if two circumferences cut, the distance of their centres...imaginary because of a negative factor, we must have one oftffie conditions d £_ r' — r, d 7 r + r', d £_ r' — r; *4- ' so that two circumferences can... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...the other side of it. Cor. 2. Hence, if two circles cut one another, the straight line which joins their centres must be less than the sum, and greater than the difference of their radii. (I. 10.) PROP. 10. If the circumferences of two areles do not meet one another in any... | |
 | John Radford Young - Conic sections - 1830 - 342 pages
...ellipse. As the distance, F'N, of the centres from which the arcs intersecting in G are described is less than the sum, and greater than the difference, of the radii, (Geom.p. 19, J it follows (28) that these arcs intersect also in another point, and thus two tangents... | |
 | John Radford Young - Conic sections - 1830 - 390 pages
...ellipse. As the distance, F'N, of the centres from which the arcs intersecting in G are described is less than the sum, and greater than the difference, of the radii, (Geom.p. 19,) it follows (28) that these arcs intersect also in another point, and thus two tangents... | |
 | Mathematics - 1835 - 684 pages
...the other side of it Cor. 2. Hence, if two circles "cut one another, the straight line which joins their centres must be less than the sum, and greater than the difference of their radii. (I. 10.) PROP. 10. If the circumferences of two circles do not meet one another in any... | |
 | John Radford Young - Geometry, Analytic - 1848 - 300 pages
...must obviously subsist the conditions r -|- d ~7 r, r + r' ~7 d, r + d ~7 r, which prove that if two circumferences cut, the distance of their centres must be less than the turn, and greater than the difference of the radii. In the second case where y becomes imaginary because... | |
 | John Radford Young - Geometry, Analytic - 1850 - 294 pages
...ellipse... As the distance, FxN, of the centres from which the arcs intersecting in G are described is less than the sum, and greater than the difference, of the radii, (Geom. p. 19,) it follows (28) that these arcs intersect also in another point, and thus two tangents... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...radii. 3d. They may cut each other, having two points common, when the distance between the centers is less than the sum and greater than the difference of the radii. 4th. One may be within the other and tangent, having one point common, when the distance between the... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...radii. 3d. They may cut each other, having two points common, when the distance between the centers is less than the sum and greater than the difference of the radii. 4th. One may be within the other and tangent, having one point common, when the distance between the... | |
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They may cut each other, having two points common, when the distance between the centers is less than the sum and greater than the difference of the radii. 
