| 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... | |
| 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... | |
| 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 =... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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