To say, for instance, that the area of a right-angled triangle is half the area of the rectangle contained by the two sides, is not to say what the area is, but what it is the half of.
The district of Bugey occupies the triangle formed by the Rhone in the south-east of the department.
For when a triangle "moves," the points do not move with it.
Its form is approximately that of an isosceles triangle, with the sharp angle extending into Lower California, W.
Projected on to the plane of the triangle as Ee, E'e and E"e.
His shoulders and hips formed a triangle that rippled with movement.
The order in which they occur in the triangle) round a circle.
The big drum, cymbals and triangle, was used by Haydn in his Military Symphony, and Mozart in his Entfilhrung, for reasons of "local colour"; it appears as an extreme means of climax in the finale of Beethoven's 9th symphony.
If there were such a thing as a triangle contained by absolutely straight lines, its three angles would no doubt measure what Euclid says; but straight lines and true triangles nowhere exist in reruns natura.
We reach similar conclusions when we recognize that the laws of nature are general or hypothetical; not in Mill's sense (" If you had such a non-existent thing as three perfectly straight lines united in a triangle "), but in a sense noted in F.
Two lines may be drawn from this point, one to each of the two rails, in a plane normal to the rails, and the ends of these lines, where they meet the rails, may be joined to complete a triangle, which may conveniently be regarded as a rigid frame resting on the rails.
He has little to say of the inner history and policy of the kingdom of Theodoric: his interests lie, as Mommsen says, within a triangle of which the three points are Sirmium, Larissa and Constantinople.
In plan it is a triangle, protected by a double moat, and has round towers at the angles.
The Treaty of Trianon satisfied the most essential claims of Yugoslavia, by dividing the whole Banat (save a small Magyar triangle opposite the city of Szeged) between her and Rumania, and by assigning to her the whole Backa (except Baja and district), part of the Baranya (forming the angle between Drave and Danube) and the Medjumurje (between Drava and Mur).
Quadrilaterals, hexagons, &c., all of which are rectilineal figures, a triangle is "differentiated" as having three sides.
For fuller discussion reference should be made to Geometry and Trigonometry, as well as to the articles dealing with particular figures, such as Triangle, Circle, &C.
Its superficial extent is seen when the folds covering the shell are cut away and the shell removed; the external surface forms a triangle with its base bordering the pericardium, and its apex directed posteriorly and reaching to the lefthand posterior corner of the shell-chamber.
Since, however, the steppe edge on the east is somewhat indefinite, some early Moslem and other geographers have included all the Hamad in Syria, making of the latter a blunt-headed triangle with a base some 700 m.
The hypothetical radicals of acids, were denoted by squares enclosing the initial letter of the base; an alkali was denoted by a triangle, and the particular alkali by inserting the initial letter.
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.
This triangle, for the convenience of calculation, we divide into two right-angled triangles.
If the latitudes differ, we have to solve an oblique-angled spherical triangle, of which two sides and the included angle are given.
Bennigsen, now commanding the whole Russian army which with Lestocq's Prussians amounted to 100,000, also moved into winter quarters in the triangle Deutsch-Eylau-Osterode-Allenstein, and had every intention of remaining there, for a fresh army was already gathering in Russia, the 1st corps of which had reached Nur about 50 m.
If the section of the finished tube is to be a triangle, with the enamel and bore at the base, the molten mass is pressed into a V-shaped mould before it is pulled out.
If now we wish to represent the variations in some property, such as fusibility, we determine the freezing-points of a number of alloys distributed fairly uniformly over the area of the triangle, and, at each point corresponding to an alloy, we erect an ordinate at right angles to the plane of the paper and proportional in length to the freezing temperature of that alloy.
If now we cut the freezing-point surface by planes parallel to the base ABC we get curves giving us all the alloys whose freezing-point is the same; these isothermals can be projected on to the plane of the triangle and are seen as dotted lines in fig.
(iii) Right-angled triangle: sides a and b, enclosing the right angle.
(v) Triangle: one side a, distant h from the opposite angle.
In E'; the case of a parallelogram, the equivalent right,, trapezium is a rectangle; in the case of a triangle, Al it is a right-angled triangle.
One of these areas is defined by the three fortresses, La Fre, Laon and Reims, the other by the triangle, LangresDijonBesancon.
From this triangle they harried the French communications with Berlin, and to secure a winter's rest for his men Napoleon determined to bring them to action.
The 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.
The sides of the triangle slope down abruptly towards the west, more gradually towards the east; at the base stands the cone of Ayala Hill, the last outpost of the Rudnik Mountains, which extend far away to the south; and, at the apex, a cliff of Tertiary chalk, 200 ft.
In somewhat sensational and affected but prophetic words Gaj compared Illyria to a lyre, " a triangle between Skutari, Varna and Villach.
The northern part of Natal presented two faces of a triangle to the two enemies, the short base being formed by the Tugela river.
Close to the head of the triangle at Dundee and Glencoe was posted a small British force under Major-General Sir W.
It is in this book that Hero proves the expression for the area of a triangle in terms of its sides.
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.
Thus the C.P. of a rectangle or parallelogram with a side in the surface is at a of the depth of the lower side; of a triangle with a vertex in the surface and base horizontal is 4 of the depth of the base; but if the base is in the surface, the C.P. is at half the depth of the vertex; as on the faces of a tetrahedron, with one edge in the surface.
The C.P. of water lines passing through a fixed point lies on a straight line, the antipolar of the point; and thus the core of a triangle is a similar triangle of one quarter the size, and the core of a parallelogram is another parallelogram, the diagonals of which are the middle third of the median lines.
Inside 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.
8) 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.
Since the potential rises proportionately to the quantity in the conductor, the ends of these ordinates will lie on a straight line and define a triangle whose base line is a length equal to the total quantity Q and V height a length equal to the final potential V.
If, for instance, the data for the triangle are sides a and b, enclosing an angle C, the area is lab sih C.
Pascal treated these numbers in his Traite du triangle arithmetique (1665), using them to develop a theory of combinations and to solve problems in proba-, bility.
" a triangle is a three-sided rectilineal figure."
A triangle is a rectilineal figure; i.e.
She stopped in front of a small mural depicting a triangle with a form at each of the points.
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.
In the case of the triangle, for instance, b is zero, so that the area is lha.
In general outline it is an irregular triangle, with apex at Cape Guardafui.
The cities of Shanghai, Hangchow and Suchow form the three points of a triangle, each being connected with the other by canal, and trade is now open by steam between all three under the inland navigation rules.
The kasbah forms the apex of a triangle of which the quays form the base.
It may be asked, Why can God not create a triangle whose three angles shall not be equal to two right angles?
A scalene triangle abc might also be employed, or a tetrahedron.
Triangle and cymbals.