A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic SectionsMacmillan, 1862 - 326 páginas |
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Página 4
... denote the co - ordinates of P referred to OX as the axis of x , and a line through O perpendicular to OX as the axis of y . Also let 0 and be the polar co - ordinates of P. If we draw from P a perpendicular on OX , we see that x = r ...
... denote the co - ordinates of P referred to OX as the axis of x , and a line through O perpendicular to OX as the axis of y . Also let 0 and be the polar co - ordinates of P. If we draw from P a perpendicular on OX , we see that x = r ...
Página 12
... denote by m the tangent of the angle QOM or BAO , that is , the tangent of the angle which that part of the line which is above the axis of x makes with the axis of x pro- duced in the positive direction . Hence if the line through the ...
... denote by m the tangent of the angle QOM or BAO , that is , the tangent of the angle which that part of the line which is above the axis of x makes with the axis of x pro- duced in the positive direction . Hence if the line through the ...
Página 18
... denote the inclination of the axes by w . Suppose first , that the line is not parallel to either axis . Let ABD be a straight line meeting the axis of y in B. Draw a line OE through the origin parallel to ABD . In ABD draw PM parallel ...
... denote the inclination of the axes by w . Suppose first , that the line is not parallel to either axis . Let ABD be a straight line meeting the axis of y in B. Draw a line OE through the origin parallel to ABD . In ABD draw PM parallel ...
Página 20
... · Let OQ be the perpendicular from the origin on a line AB ; let OQ = p , OA = a , OB = b . If we suppose QOA = a , we have QOBw - a ; denote this by ẞ ; then OQ = P = a cosa ; ... a = 20 EQUATION IN TERMS OF THE PERPENDICULAR .
... · Let OQ be the perpendicular from the origin on a line AB ; let OQ = p , OA = a , OB = b . If we suppose QOA = a , we have QOBw - a ; denote this by ẞ ; then OQ = P = a cosa ; ... a = 20 EQUATION IN TERMS OF THE PERPENDICULAR .
Página 51
... denote by P the point of intersection of the three lines in the first proposition , by Q the point of intersection of the three lines in the second proposition , and by R the point of intersection of the three lines in the third ...
... denote by P the point of intersection of the three lines in the first proposition , by Q the point of intersection of the three lines in the second proposition , and by R the point of intersection of the three lines in the third ...
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Términos y frases comunes
a²b² a²b³ a²y abscissa asymptotes ax² axes axis of x b²x² bisects centre chord of contact circle conic section conjugate diameters conjugate hyperbola constant Crown 8vo cy² denote directrix distance Edition ellipse equa equal Examples external point find the equation find the locus fixed point focal chord focus given lines given point Hence the equation inclined latus rectum Let the equation line drawn line joining lines meet lines which pass major axis meet the curve middle point negative normal ordinate origin parabola parallel perpendicular point h point of intersection polar co-ordinates polar equation pole positive preceding article proposition radical axis radius ratio rectangular required equation respectively right angles shew shewn sides Similarly student suppose tangent tion triangle vertex x₁ y₁
Pasajes populares
Página 100 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Página 304 - Or, four terms are in harmonical proportion, when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth.
Página 25 - In this equation n is the tangent of the angle which the line makes with the axis of abscissae, and B is the intercept on this axis from the origin.
Página 141 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.
Página 189 - Hyperbola is the locus of a point which moves so that its distance from a fixed point, called the focus, bears a constant ratio, which is greater than unity, to its distance from a fixed straight line, called the directrix.