Proceedings of the Edinburgh Mathematical Society, Volume 1Scottish Academic Press, 1894 - Electronic journals |
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Common terms and phrases
2abcA a+b+c A₁ angles B₁ bisector bisects centroid circumcentre circumscribed collinear complementary triangle concyclic congruent D₁ denoted diameter distances double point draw Edinburgh Mathematical Society Eigenschaften...des...Dreiecks equal EULER'S LINE excentres excircle F₁ F₂ Feuerbach formed by joining four I triangles fundamental triangle Gentleman's Diary George Watson's College given Grunert's Archiv H₁ H₂ Hence homothetic centre incentre incircle inscribed internal bisector intersect isosceles Lady's and Gentleman's m₁ Mathematical Master medians meet the circumcircle mid point nine-point circle oppositely situated orthic tetrastigm orthic triangle orthocentre parallel to BC parallelogram perpendicular to BC point of BC point of concurrency proof r₁ radii radius rectangle rhombi semiperimeter sides similar Similarly square T. S. Davies tangents theorem triangle ABC triangle DEF triangle formed V₁ vertices
Popular passages
Page 52 - The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair.
Page 47 - The six straight lines joining two and two the centres of the four circles which touch the sides of a triangle pass each through one of the vertices of the triangle.
Page 34 - Compare the area of the triangle formed by joining the centres of these squares with the area of the equilateral triangle.
Page 37 - If two triangles have two sides of the one equal to two sides of the...
Page 14 - Wherefore, if the ratios &c. EXERCISES. 1. Shew that the locus of the middle points of straight lines parallel to the base of a triangle and terminated by its sides is a straight line. 2. CAB, CEB are two triangles having the angle B common and the sides CA, CE equal ; if BAE be produced to D and ED be taken a third proportional to BA , AC, then the triangle BDC is similar to the triangle BAC.
Page 60 - If the perpendicular from any vertex of a triangle to the opposite side divides that side into two segments, how does each of these segments compare in length with its adjacent side of the triangle ? Prove it.
Page 20 - GT-JAB is a maximum, that is, when GBC x GCA x GAB is a maximum, that is, when these three triangles are equal, that is, when G is the centroid. (24) If three straight lines drawn from the vertices of a triangle are concurrent, the three straight lines drawn parallel to them from the mid points of the opposite sides are also concurrent ; and the straight line joining the two points of concurrency passes through the centroid of the triangle and is there trisected. J The triangles ABC, A'B'C' are similar...
Page 98 - Conies, p. 54, that if the perpendiculars from the vertices of one triangle on the sides of another meet in a point, so will the perpendiculars from the vertices of the second on the sides of the first.
Page 51 - Hence the differences between the angles of the successive triangles become always a smaller and smaller fraction of the differences between the angles of the original triangle ; the successive triangles therefore approximate to an equilateral triangle.
Page 101 - A 6> fccosB nc* ccosC = 0. 17486. (HD DRURY, MA) — Prove geometrically that the sum of the distances of the orthocentre of a triangle from the vertices is equal to the sum of the diameters of the in-circle and circum-circle. 17487.