Its form is approximately that of an isosceles triangle, with the sharp angle extending into Lower California, W.
Turning, 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.
If both places have the same latitude we have to deal with an isosceles triangle, of which two sides and the included angle are given.
Take 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.
In 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).
Plato (Timaeus) described the figure in the following terms: - "The isosceles triangle which has its vertical angle a right angle.
6, ABC is an isosceles triangle right D FIG.
P. 157); (2) the angles at the base of an isosceles triangle are equal (Id.
32 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.
A 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.
The 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.
Now I feel as if I should succeed in doing something in mathematics, although I cannot see why it is so very important to know that the lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal!