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" ... where r, s, t are the distances of any point on the curve from the three foci. We shall enter into more detail on this subject in the next Chapter. Ex. 4. Equations of the form just mentioned include many well-known curves of the fourth degree. For... "
A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ... - Page 127
by George Salmon - 1852 - 316 pages
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A System of Algebraic Geometry, Volume 1

Dionysius Lardner - Geometry, Algebraic - 1823 - 658 pages
...being positive for the ellipse, and negative for the hyperbola. (210.) Cor. I. Hence, an ellipse is the locus of the vertex of a triangle, of which the base and sum of the sides are given ; and ' an hyperbola is the locus, when the base and difference of the sides...
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A Treatise on Algebraic Geometry

Dionysius Lardner - Geometry, Algebraic - 1831 - 512 pages
...being positive for the ellipse, and negative for the hyperbola. (210.) Cor. I. Hence, an ellipse is the locus of the vertex of a triangle, of which the base and sum of the sides are given ; and an hyperbola is the locus, when the base and difference of the sides...
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A Treatise on the Higher Plane Curves: Intended as a Sequel to A Treatise on ...

George Salmon - Conic sections - 1852 - 338 pages
...three of which have the property, in the first case, Ir + ms = (I + m) t ; in the second case, lr+ms + nt= 0, where r, s, t are the distances of any point...origin, the given rectangle being ab, the equation is (X* + y1 + a2 - 2ax) (tf + y2 + a2 + 2a#) = a262, or (#2 + y2)2 + 2aa(>2 + y2) - 4a'V + a4 - a?b2 =...
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Lectures on Quaternions: Containing a Systematic Statement of a New ..., Part 1

Sir William Rowan Hamilton - Quaternions - 1853 - 890 pages
...; centre of mean distances, or of gravity, ft = . aa -r- a ; investigation of the (spherical) locus of the vertex of a triangle, of which the base and the ratio of the sides are given; T(<r-y) =T(*<ry), if Tff=Ty, . . . Articles 456 to 459 ; Pages...
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A Dictionary of Science, Literature, & Art: Comprising the ..., Volume 1

William Thomas Brande - Encyclopedias and dictionaries - 1867 - 974 pages
...common example is the Ciissida eyuestria of Fabricius. Casstnlan Ovals. Such an oval may be defined as the locus of the vertex of a triangle of which the base and rectangle under the sides are given. Taking the hasp (2) as axis and its middle point as pole, the equation is clearly...
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Dublin examination papers

Dublin city, univ - 1871
...of the evolute of the curve py2 — xa = o. 1 8. Find the position of the foci of the curve which is the locus of the vertex of a triangle of which the base and rectangle under sides are given. Classi<s. ARISTOTLE. MR. TYRRELL. Translate the following passages : — 1. Bet/inning, To S1 dKovaiov...
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An elementary manual of coordinate geometry and conic sections

James White - Conic sections - 1878 - 160 pages
...describe an ellipse. The two fixed points are called the/oei. The ellipse may therefore be defined as the locus of the vertex of a triangle of which the base and the sum of the sides are given, the extremities of the base being the foci. This property of the curve...
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Calendar

University of Sydney - 1904
...Find an expression for the tangent of the angle between two given straight lines. Obtain analytically the locus of the vertex of a triangle, of which the base and vertical angle are given. 5. Find the equation to the circle which passes through the origin, and cuts...
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