An Elementary Treatise on the Application of the Algebraic Analysis to Geometry, Parte 1Geo. Greenhill ... and also by W. Glendinning, 1831 - 52 páginas |
Outras edições - Ver todos
An Elementary Treatise on the application of the Algebraic Analysis to Geometry Wesley Stoker Barker Woolhouse Visualização completa - 1831 |
An Elementary Treatise on the Application of the Algebraic Analysis to ... Wesley Stoker Barker Woolhouse Prévia não disponível - 2017 |
Termos e frases comuns
A—B)²+C² AB-C² Algebraic Analysis asymptote is parallel ax+by+c ax+by+c=0 axis of x circle of curvature constant convex or concave corresponding cos² curve being given d²s)² d²y d²y)² d³y denote determined different signs differentials dr² ds² dx dy dx² dy d²x dy² ellipse equa evidently evolute find the length formulæ given angle given line given point x'y given to find hence hyperbola inclination indefinitely infinite involute involving Let x'y locus normal obviously ordinates osculating circle perpendicular point of contact polar angle polar equation positive or negative principal diameters principal semi-diameters r²d r²dq² radius of curvature radius vector rd²r rectangular axes rectangular co-ordinates similarly sin² straight line substituting subtangent supposing tan w tangent thence values variable wherein x²+B y=mx+h
Passagens mais conhecidas
Página 43 - Find an expression for the radius of curvature in terms of the radius vector and the perpendicular on the tangent.
Página 16 - J'2' That is, the sum of the reciprocals of the squares of any two semi-diameters of a curve of the second order, which are perpendicular to each other, is the same ; and, in reference!
Página 19 - V -AB, the values of the constants A, B must have the same sign to make C real, that is, they must be either both of them positive or both negative ; and hence we may consider them both positive for, when negative, they can be made so by preliminarly changing all the signs of the original equation.
Página 15 - A", B" have different signs. 59. 9th. In the two following cases it will be found that no real values of x and y can possibly fulfil the equation (b) • and consequently that the equation can have no locus. First. When G and 4 AB — C2 are of the same sign and A", B
Página 19 - ... it must coincide with the axis of the curve. Therefore the above equation properly represents the principal diameter of the curve; by uniting it with the original equation we may hence find the co-ordinates x'y' of its intersection with the curve, or the vertex.
Página 11 - B, C, a, b, c, may be either positive or negative, Let us in the first place transfer the equation to two other rectangular axes parallel to the original ones and having their origin at a point whose ordinates are ab; and, (43,) by substituting x -\- x...
Página 18 - We have, (63,) assumed x'y' to determine a point in the curve, but not restricted ourselves to any particular point; •we may therefore take this point where the curve is intersected by a straight line whose equation is by means of which we shall have ,V^+S^B+ which reduces the equation to ^.* = o....(c).