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isosceles

p. 157); (2) the angles at the base of an isosceles triangle are equal (Id.

68366, ABC is an isosceles triangle right D FIG.

4943Take any two arbitrary directions in the plane of the paper, and draw a small isosceles triangle abc, whose sides are perpendicular to the two directions, and consider the equilibrium of a small triangular prism of fluid, of which the triangle is the cross section.

3226Take any two arbitrary directions in the plane of the paper, and draw a small isosceles triangle abc, whose sides are perpendicular to the two directions, and consider the equilibrium of a small triangular prism of fluid, of which the triangle is the cross section.

3226If both places have the same latitude we have to deal with an isosceles triangle, of which two sides and the included angle are given.

2931Its form is approximately that of an isosceles triangle, with the sharp angle extending into Lower California, W.

2328Turning, therefore, to a globe, Asia, viewed as a whole, will be seen to have the form of a great isosceles spherical triangle, having its north-eastern apex at East Cape (Vostochnyi), in Bering Strait; its two equal sides, in length about a quadrant of the sphere, or 6500 m., extending on the west to the southern point of Arabia, and on the east to the extremity of the Malay peninsula; and the base between these points occupying about 60° of a great circle, or 4 500 m., and being deeply indented by the Arabian Sea and the Bay of Bengal on either side of the Indian peninsula.

192732 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.

1221A formula such as the equality of the interior angles of a triangle to two right angles is only scientifically known when it is not of isosceles or scalene triangle that it is known, nor even of all the several types of triangle collectively, but as a predicate of triangle recognized as the widest class-concept of which it is true, the first stage in the progressive differentiation of figure at which it can be asserted.° Three points obviously need development, the nature of definition, its connexion with the syllogism in which the middle term is cause or ground, and the way in which we have assurance of our principles.

616The spherical A isosceles triangles AJB, BJC are con gruent, and we see that AB can be brought into the position BC by a rotation about the axis OJ through an FIG.

514thick of a monolithic dam, subject to the pressure of water against its vertical side to the full depth ab= d in feet, the horizontal _ eL 2 pressure of water against the section of the dam, inI creasing uniformly with the depth, is properly represented by the isosceles right-angled triangle abe, in which be is the maximum water-pressure due to the Cent full depth d, while the area 2 abe = d is t h e total hor12 d3 6 If x be the width of the base, and p the density of the masonry, the weight of the masonry in terms of a cubic foot of water will be acting at its centre of gravity g, situated at 3x from the outer toe, and the moment of resistance to overturning on the outer toe, p x 2 d (2) In countries where good clay or retentive earth cannot be obtained, numerous alternative expedients have been adopted with more or less success.

412As the Greek philanderer isosceles used to say, " There are 3 sides to every triangle " .

00isosceles triangle with a altitude drawn.

00isosceles trapezium (trapezoid in American usage) in which three of the sides have the same length.

00isosceles position in which recoil is evident.

00Being either isosceles or scalene is inseparable from a triangle in real existence.

00The demihexagon is an isosceles trapezium (trapezoid in American usage) in which three of the sides have the same length.

00To see this, imagine an isosceles triangle with a altitude drawn.

00Its form is approximately that of an isosceles triangle, with the sharp angle extending into Lower California, W.

00Turning, therefore, to a globe, Asia, viewed as a whole, will be seen to have the form of a great isosceles spherical triangle, having its north-eastern apex at East Cape (Vostochnyi), in Bering Strait; its two equal sides, in length about a quadrant of the sphere, or 6500 m., extending on the west to the southern point of Arabia, and on the east to the extremity of the Malay peninsula; and the base between these points occupying about 60Ã‚° of a great circle, or 4 500 m., and being deeply indented by the Arabian Sea and the Bay of Bengal on either side of the Indian peninsula.

00If both places have the same latitude we have to deal with an isosceles triangle, of which two sides and the included angle are given.

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).

00Plato (Timaeus) described the figure in the following terms: - "The isosceles triangle which has its vertical angle a right angle.

006, ABC is an isosceles triangle right D FIG.

00p. 157); (2) the angles at the base of an isosceles triangle are equal (Id.

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.

00A formula such as the equality of the interior angles of a triangle to two right angles is only scientifically known when it is not of isosceles or scalene triangle that it is known, nor even of all the several types of triangle collectively, but as a predicate of triangle recognized as the widest class-concept of which it is true, the first stage in the progressive differentiation of figure at which it can be asserted.Ã‚° Three points obviously need development, the nature of definition, its connexion with the syllogism in which the middle term is cause or ground, and the way in which we have assurance of our principles.

00The spherical A isosceles triangles AJB, BJC are con gruent, and we see that AB can be brought into the position BC by a rotation about the axis OJ through an FIG.

00thick of a monolithic dam, subject to the pressure of water against its vertical side to the full depth ab= d in feet, the horizontal _ eL 2 pressure of water against the section of the dam, inI creasing uniformly with the depth, is properly represented by the isosceles right-angled triangle abe, in which be is the maximum water-pressure due to the Cent full depth d, while the area 2 abe = d is t h e total hor12 d3 6 If x be the width of the base, and p the density of the masonry, the weight of the masonry in terms of a cubic foot of water will be acting at its centre of gravity g, situated at 3x from the outer toe, and the moment of resistance to overturning on the outer toe, p x 2 d (2) In countries where good clay or retentive earth cannot be obtained, numerous alternative expedients have been adopted with more or less success.

00

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