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equilateral

In a similar manner, four covertical equilateral triangles stand on a square base.

11634If the faces be all equal equilateral triangles the solid is termed the "regular" tetrahedron.

533432 was first proved in a general way by the Pythagoreans; but, on the other hand, we learn from Geminus that the ancient geometers observed the equality to two right angles in each kind of triangle - in the equilateral first, then in the isosceles, and lastly in the scalene (Apoll.

3532Five equilateral triangles covertically placed would stand on a pentagonal base, and it was found that, by forming several sets of such pyramids, a solid could be obtained which had zo triangular faces, which met in pairs to form 30 edges, and in fives to form 12 vertices.

2822Ladenburg (Ber., 2, p. 140) devised his prism formula (IV), the six carbon atoms being placed at the six corners of a right equilateral triangular prism, with its plane projections (V, VI).

2322The regular octahedron has for its faces equilateral triangles; it is the reciprocal of the cube.

1920Unicardiidae.-Shell sub-orbicular, nearly equilateral, with concentric striae.

1624Nicaragua forms an irregular equilateral triangle with its base stretching for 280 m.

1416Nicaragua forms an irregular equilateral triangle with its base stretching for 280 m.

1316The theorem, then, seems to have been arrived at by induction, and may have been suggested by the contemplation of floors or walls covered with tiles of the form of equilateral triangles, or squares, or hexagons.

1321The equilateral triangle is the basis of the tetrahedron, octahedron and icosahedron.'

1214Inside an equilateral triangle, for instance, of height h, - 2Ra/3y/h, (8) where a, 13, y are the perpendiculars on the sides of the triangle.

1220Octahedra having triangular faces other than equilateral occur as crystal forms. See Polyhedron and Crystallography.

1119Incidentally Pappus describes the thirteen other polyhedra bounded by equilateral and equiangular but not similar polygons, discovered by Archimedes, and finds, by a method recalling that of Archimedes, the surface and volume of a sphere.

1016A third reflecting plate is sometimes employed, the cross-section of the three forming an equilateral triangle.

10198) be an equilateral triangle, the angular points corresponding to the three pure metals A, B, C. C Then the composition of any alloy can be FIG.

916Warren type in which the bracing bars form equilateral triangles, the Whipple Murphy in which the struts are vertical and the ties inclined, and the lattice in which both struts and ties are inclined at equal angles, usually 45° with the horizontal.

9168) be an equilateral triangle, the angular points corresponding to the three pure metals A, B, C. C Then the composition of any alloy can be FIG.

916Division of the nucleolus by elongation, construction, and equilateral division of the nucleus.

918V = 3rA = 2 1 4 / 3 n F tan -II cot e a = 2 I 1 3 n F cot e a cos a/ (sin' a -cos t 13) 2 R =1-/ tan IT tan 0=1/ sin 13/(sin e a-cost r =Zl tan 21 cot a= Il cot a cos 13/(sin" a -cos' (3)L 1 In the language of Proclus, the commentator: " The equilateral triangle is the proximate cause of the three elements, ` fire,' ` air ' and ` water '; but the square is annexed to the ` earth.'

816The names of these five solids are: (r) the tetrahedron, enclosed by four equilateral triangles; (2) the cube or hexahedron, enclosed by 6 squares; (3) the octahedron, enclosed by 8 equilateral triangles; (4) the dodecahedron, enclosed by 12 pentagons; (5) the icosahedron, enclosed by 20 equilateral triangles.

712The French army was thus disposed almost in an equilateral triangle with sides of about 570 m., with 95,000 men at the apex at Moscow opposed to 120,000, 30,000 about Brest opposite ioo,000, and 17,000 about Drissa confronted by 40,000, whilst in the centre of the base at Smolensk lay Victor's corps, about 30,000.

716The isothermals are approximately equilateral hyperbolas (pv= constant), with the axes of p and v for asymptotes, for a gas or unsaturated vapour, but coincide with the isopiestics for a saturated vapour in presence of its liquid.

716These problems were also attacked by the Arabian mathematicians; Tobit ben Korra (836-901) is credited with a solution, while Abul Gud solved it by means of a parabola and an equilateral hyperbola.

716The French army was thus disposed almost in an equilateral triangle with sides of about 570 m., with 95,000 men at the apex at Moscow opposed to 120,000, 30,000 about Brest opposite ioo,000, and 17,000 about Drissa confronted by 40,000, whilst in the centre of the base at Smolensk lay Victor's corps, about 30,000.

716If three equilateral triangles be placed at a common vertex with their covertical sides coincident in pairs, it is seen that the base is an equal equilateral triangle; hence four equal equilateral triangles enclose a space.

613Dimyarian, with orbicular and almost equilateral shell; adherent; hinge without teeth Sand ligament internal.

615In the case of a biaxal plate perpendicular to the bisector of the acute angle between the optic axes, the curves of constant retardation are approximately Cassini's ovals, and the lines of like polarization are equilateral hyperbolae passing through the points corresponding to the optic axes.

412equilateral triangle or square.

00equilateral faces are dimpled.

00Omega Centauri makes an almost equilateral triangle with these two stars on their western side.

00While this design may have been traditional, the shape of the new 50p coin, an equilateral curve heptagon, was revolutionary.

00Finally, we get down to our first proposition: Proposition 1. On a given straight line to construct an equilateral triangle.

00The base of the equilateral triangle is the top of the wedge.

00If the faces be all equal equilateral triangles the solid is termed the "regular" tetrahedron.

00A third reflecting plate is sometimes employed, the cross-section of the three forming an equilateral triangle.

00Ladenburg (Ber., 2, p. 140) devised his prism formula (IV), the six carbon atoms being placed at the six corners of a right equilateral triangular prism, with its plane projections (V, VI).

00In shape roughly resembling an equilateral triangle, with base uppermost, Bosnia and Herzegovina cover an area of 19,696 sq.

00Division of the nucleolus by elongation, construction, and equilateral division of the nucleus.

00Inside an equilateral triangle, for instance, of height h, - 2Ra/3y/h, (8) where a, 13, y are the perpendiculars on the sides of the triangle.

00(7) For example, in the equilateral triangle of (8) § 28, referred to coordinate axes made by the base and height, = -2 Ra,(3y/h= - 1.

00The following method, depending on the constancy of the sum of the perpendiculars from any point on to the sides of an equilateral triangle, can be adopted: - Let ABC (fig.

00The isothermals are approximately equilateral hyperbolas (pv= constant), with the axes of p and v for asymptotes, for a gas or unsaturated vapour, but coincide with the isopiestics for a saturated vapour in presence of its liquid.

00In crystallography the icosahedron is a possible form, but it has not been observed; it is closely simulated by a combination of the octahedron and pentagonal dodecahedron, which has twenty triangular faces, but only eight are equilateral, the remaining twelve being isosceles (see Crystallography).

00These problems were also attacked by the Arabian mathematicians; Tobit ben Korra (836-901) is credited with a solution, while Abul Gud solved it by means of a parabola and an equilateral hyperbola.

00Warren type in which the bracing bars form equilateral triangles, the Whipple Murphy in which the struts are vertical and the ties inclined, and the lattice in which both struts and ties are inclined at equal angles, usually 45Ã‚° with the horizontal.

00Dimyarian, with orbicular and almost equilateral shell; adherent; hinge without teeth Sand ligament internal.

00Unicardiidae.-Shell sub-orbicular, nearly equilateral, with concentric striae.

00The regular octahedron has for its faces equilateral triangles; it is the reciprocal of the cube.

00Octahedra having triangular faces other than equilateral occur as crystal forms. See Polyhedron and Crystallography.

00Incidentally Pappus describes the thirteen other polyhedra bounded by equilateral and equiangular but not similar polygons, discovered by Archimedes, and finds, by a method recalling that of Archimedes, the surface and volume of a sphere.

0032 was first proved in a general way by the Pythagoreans; but, on the other hand, we learn from Geminus that the ancient geometers observed the equality to two right angles in each kind of triangle - in the equilateral first, then in the isosceles, and lastly in the scalene (Apoll.

00The theorem, then, seems to have been arrived at by induction, and may have been suggested by the contemplation of floors or walls covered with tiles of the form of equilateral triangles, or squares, or hexagons.

00P the octahedron faces; the latter are particularly well defined and have the form =% of equilateral triangles (fig.

00Although the pointed arches used are sometimes equilateral and sometimes drop-arches, the lancet-arch is the most characteristic. The period is best recognized in England by the great depth given to the hollows of the mouldings, alternating with fillets and rolls, by the decoration of the hollows with the dog-tooth ornament, by the circular abacus of the capitals, and the employment of slender detached shafts of Purbeck marble which are attached to piers by circular moulded shaftrings (Fr.

00The names of these five solids are: (r) the tetrahedron, enclosed by four equilateral triangles; (2) the cube or hexahedron, enclosed by 6 squares; (3) the octahedron, enclosed by 8 equilateral triangles; (4) the dodecahedron, enclosed by 12 pentagons; (5) the icosahedron, enclosed by 20 equilateral triangles.

00The equilateral triangle is the basis of the tetrahedron, octahedron and icosahedron.'

00If three equilateral triangles be placed at a common vertex with their covertical sides coincident in pairs, it is seen that the base is an equal equilateral triangle; hence four equal equilateral triangles enclose a space.

00In a similar manner, four covertical equilateral triangles stand on a square base.

00Five equilateral triangles covertically placed would stand on a pentagonal base, and it was found that, by forming several sets of such pyramids, a solid could be obtained which had zo triangular faces, which met in pairs to form 30 edges, and in fives to form 12 vertices.

00V = 3rA = 2 1 4 / 3 n F tan -II cot e a = 2 I 1 3 n F cot e a cos a/ (sin' a -cos t 13) 2 R =1-/ tan IT tan 0=1/ sin 13/(sin e a-cost r =Zl tan 21 cot a= Il cot a cos 13/(sin" a -cos' (3)L 1 In the language of Proclus, the commentator: " The equilateral triangle is the proximate cause of the three elements, ` fire,' ` air ' and ` water '; but the square is annexed to the ` earth.'

00In the case of a biaxal plate perpendicular to the bisector of the acute angle between the optic axes, the curves of constant retardation are approximately Cassini's ovals, and the lines of like polarization are equilateral hyperbolae passing through the points corresponding to the optic axes.

00Finally, we get down to our first proposition: Proposition 1. On a given straight line to construct an equilateral triangle.

00The base of the equilateral triangle is the top of the wedge.

00

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