# Triangles Sentence Examples

- If the faces be all equal equilateral
**triangles**the solid is termed the "regular" tetrahedron. - Arrangements connected with Claus' formula are obtained by placing six tetrahedra on the six
**triangles**formed by the diagonals of a plane hexagon. - 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. - The arc measured was 3° 7' 3" in length; and the work consisted of two measured bases connected by a series of
**triangles**, one north and the other south of the equator, on the meridian of Quito. - Contains problems of finding rational right-angled
**triangles**such that different functions of their parts (the sides and the area) are squares. - The investigation of
**triangles**and other figures drawn upon the surface of a sphere is all-important in the sciences of astronomy, geodesy and geography. - The artificial character of the diction renders it in emotional passages stilted and even absurd, and makes Canning's clever caricature - The Loves of the
**Triangles**- often remarkably like the poem it satirizes: in some passages, however, it is not without a stately appropriateness. - The quadrilateral, for instance, consists of two
**triangles**, and its area is the product of half the length of one diagonal by the sum of the perpendiculars drawn to this diagonal from the other two angular points. - In "geodesy," and the cognate subject "figure of the earth," the matter of greatest moment with regard to the sphere is the determination of the area of
**triangles**drawn on the surface of a sphere - the so-called "spherical**triangles**"; this is a branch of trigonometry, and is studied under the name of spherical trigonometry. - Warren 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. - If there are no redundant members in the frame there will be only two members abutting at the point of support, for these two members will be sufficient to balance the reaction, whatever its direction may be; we can therefore draw two
**triangles**, each having as one side the reaction YX, and having the two other sides parallel to these two members; each of these**triangles**will represent a polygon of forces in equilibrium at the point of support. - Of these two
**triangles**, shown in fig. - Legendre was also the author of a memoir upon
**triangles**drawn upon a spheroid. - 2 The method consists in the use of the formula sin a sin b=2 {cos(a-b)-cos(a+b)l, by means of which the multiplication of two sines is reduced to the addition or subtraction of two tabular results taken from a table of sines; and, as such products occur in the solution of spherical
**triangles**, the method affords the solution of spherical**triangles**in certain cases by addition and subtraction only. - Wittich in 1584 made known at Cassel the calculation of one case by this prosthaphaeresis; and Justus Byrgius proved it in such a manner that from his proof the extension to the solution of all
**triangles**could be deduced.3 Clavius generalized the method in his treatise De astrolabio (1593), lib. - The fourth book deals with the circle in its relations to inscribed and circumscribed
**triangles**, quadrilaterals and regular polygons. - The regular octahedron has for its faces equilateral
**triangles**; it is the reciprocal of the cube. - The city park system includes Ottawa Park (280 acres), Bay View Park (202 acres), Riverside Park (118 acres), Central Grove Park (loo acres), Collins Park (90 acres), Walbridge Park (67 acres), with a zoological collection, Navarre Park (53 acres), several smaller parks and
**triangles**, and a boulevard, 18 m. - The 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. - [3] Thales discovered the theorem that the sides of equiangular
**triangles**are proportional. - In applying tests of memory, it may be legitimate to allow a candidate to pass who answers correctly from 30 to 50% of the questions; such an allowance if applied to a test of capacity, such as the performance of a sum in addition, the solution of
**triangles**by means of trigonometrical tables, or the translation of an easy passage from a foreign language, appears to be irrational. - This follows from the fact that all such
**triangles**are necessarily similar. - The relation between the three forces acting on any particle, viz, the extraneous force and the tensions in the two adjacent portions of the string can be exhibited by means of a triangle of forces; and if the successive
**triangles**be drawn to the same scale they can be fitted together so as to constitute a single force-diagram, as shown in fig. - 16) represent the two forces, AD their resultant; we have to prove that the sum of the
**triangles**OAB, OAC is D equal to the triangle OAD, - The
**triangles**OAB, RHK are similar, and if the perpendiculars OM, RN be drawn we have HK .OM~rAB. - Successive
**triangles**in the diagram of forces may be constructed in the order XYZ, ZXA, AZB. - 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. - If we construct a, the spherical
**triangles**ABC, - The spherical
**triangles**ABC, ABC - The composition of finite rotations about parallel axes is, a particular case of the preceding; the radius of the sphere is now infinite, and the
**triangles**are plane. - Further, at any one of the centres of load let PL represent the magnitude and direction of the gross load, and Pa, Pb the two resistances by which the piece to which that load is applied is supported; then wifl those three lines be respectively the diagonal and sides of a parallelogram; or, what is the same thing, they will be equal to the three sides of a
**triangleS**and they must be in the same plane, although the sides of the polygon of resistances may be in different planes. - Or because of the proportionality of the sides of
**triangles**to the sines of the opposite angles, sin TOB: sin TOA: sin AOB:: a: ~: y, (8 A~ - For, let PiP~ cut the line of centres at I; then, by similar
**triangles**, CiP2 C1Pi IC2: ICi; (24) - That the
**triangles**CbD and DcE are .~ - From the great Indus series of
**triangles**bases have been selected at intervals which have supported minor chains of triangulation reaching into the heart of the country. - Identity and difference among ideas, as when we say that " blue is not yellow "; or (b) with mathematical relations, as that " two
**triangles**upon equal bases between two parallels must be equal "; or (c) in assertions that one quality does or does not coexist with another in the same substance, as that " iron is susceptible of magnetical impressions, or that ice is not hot "; or (d) with ontological reality, independent of our perceptions, as that " God exists " or " I exist " or " the universe exists." - The 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**. - If 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. - In a similar manner, four covertical equilateral
**triangles**stand on a square base. - Five 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. - That the triangle could give rise to no other solid followed from the fact that six covertically placed
**triangles**formed a plane. - Cayley gave the formula E + 2D = eV + e'F, where e, E, V, F are the same as before, D is the same as Poinsot's k with the distinction that the area of a stellated face is reckoned as the sum of the
**triangles**having their vertices at the centre of the face and standing on the sides, and e' is the ratio: " the angles subtended at the centre of a face by its sides /2rr." - The snub cube is a 38-faced solid having at each corner 4
**triangles**and I square; 6 faces belong to a cube, 8 to the coaxial octahedron, and the remaining 24 to no regular solid. - The pentagons belong to a dodecahedron, and 20
**triangles**to an icosahedron; the remaining 60**triangles**belong to no regular solid. - Now, madam, these
**triangles**are equal; please note that the angle ABC... - The fact that the interior angles of all
**triangles**are equal to two right angles is not part of the definition, but is universally true. - For figures of more than four sides this method is not usually convenient, except for such special cases as that of a regular polygon, which can be divided into
**triangles**C by radii drawn from its centre. - Take any point P in the latter, and form
**triangles**by joining P to each of the sides AB, BC, ... - Then (as the difference of two
**triangles**) area ABCD - (h cot 2 (h cot -a)2 2(cot ¢- cot 4) 2(cot +cot 0) (ii) If 0=0, this becomes tan area (h + a tan 0) 2 - a tan 0. - Then AD =EB = 2h, and the
**triangles**AVD and BVE are equal. - Over and above these there are other marks, crosses,
**triangles**, &c., of which more than a hundred have been described and figured by different authors, each with its interpretation; and in addition the back of the hand has its ridges.