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The polygons adopted were of 20 or more sides approximating to a circular form.

189These have faces which are all regular polygons, but not all of the same kind, while all their solid angles are equal.

94- These solids have all their faces equal regular polygons, and the angles at the vertices all equal.

63" Regular polyhedra " are such as have their faces all equal regular polygons, and all their solid angles equal; the term is usually restricted to the five forms in which the centre is singly enclosed, viz.

52- These solids are characterized by having all their angles equal and all their faces regular polygons, which are not all of the same species.

41Partial Polygons of Resistance.In a structure in which there are pieces supported at more than two joints, let a polygon be con-.

42They bear a relation to the Platonic solids similar to the relation of " star polygons " to ordinary regular polygons, inasmuch as the centre is multiply enclosed in the former and singly in the latter.

42Partial Polygons of Resistance.In a structure in which there are pieces supported at more than two joints, let a polygon be con-.

42The latter, as we know, calculated the perimeters of successive polygons, passing from one polygon to another of double the number of sides; in a similar manner Gregory calculated the areas.

43Hero's expressions for the areas of regular polygons of from 5 to 12 sides in terms of the squares of the sides show interesting approximations to the values of trigonometrical ratios.

32As regards the funicular diagram, let LM be the line on which the pairs of corresponding sides of the two polygons meet, and through it draw any two planes w, w.

32and the corresponding polygons in the other figure by the same letters; a line joining two points A, B in one figure will then correspond to the side common to the two polygons A, B in the other.

32The stresses produced by extraneous forces in a simple frame can be found by considering the equilibrium of the various joints in a proper succession; and if the graphical method be employed the various polygons of force can be combined into a single force-diagram.

32By constructing several partial polygons, and computing the relations between the loads and resistances which are determined by the application of that theorem to each of them, with the aid, if necessary, of Moseleys principle of the least resistance, the whole of the relations amongst the loads and resistances may be found.

32In drawing these polygons the magnitude of the vector of the type Wr is the product Wr, and the direction of the vector is from the shaft outwards towards the weight W, parallel to the radius r.

32Relations between Polygons of Loads and of Resistances.In a structure in which each piece is supported at two joints only, the well-known laws of statics show that the directions of the gross load on each piece and of the two resistances by which it is supported must lie in one plane, must either be parallel or meet in one point, and must bear to each other, if not parallel, the proportions of the sides of a triangle respectively parallel to their directions, and, if parallel, such proportions that each of the three forces shall be proportional to the distance between the other two,all the three distances being measured along one direction.

23Incidentally 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.

25The fourth book deals with the circle in its relations to inscribed and circumscribed triangles, quadrilaterals and regular polygons.

10It must be remembered that these are all directed quantitie~, and that their respective sums are to be taken by drawing vector polygons.

10These figures are often termed " semi-regular solids," but it is more convenient to restrict this term to solids having all their angles, edges and faces equal, the latter, however, not being regular polygons.

10Although this term is frequently given to the Archimedean solids, yet it is a convenient denotation for solids which have all their angles, faces, and edges equal, the faces not being regular polygons.

10For shaded polygons, the color keyword can specify an array that contains the color index at each vertex.

10Most hardware accelerators will directly render polygons to scenes therefore freeing up processor time for other tasks.

10Most hardware accelerators will directly render polygons to scenes freeing up processor time for other tasks.

10find the centroid coordinates for all of the polygons, then press the middle button on the mouse to quit.

10Points, lines, polygons, circles, arcs, and smooth curves can be freely intermixed with text.

10Geometrical optics are a useful tool for calculating reflections from the polygons in a 3D database.

10In the same way games were revolutionized with the advent of 3D polygons, they will be revolutionized again with VR.

10The main problem with frequency polygons is deciding what to do with the endpoints.

10These store the image as a set of graphic primitives; shapes such as lines, ellipses, rectangles and polygons.

10sliver polygons automatically.

10We'll also be making sure all the polygons have four vertices (called quads ).

10Inscribing in and circumscribing about a circle two polygons, each of ninety-six sides, and assuming that the perimeter of the circle lay between those of the polygons, he obtained the limits he has assigned by sheer calculation, starting from two close approximations to the value of 1 / 3, which he assumes as known (265/153 < A t 3 < 1351/780).

00Hero's expressions for the areas of regular polygons of from 5 to 12 sides in terms of the squares of the sides show interesting approximations to the values of trigonometrical ratios.

00The polygons adopted were of 20 or more sides approximating to a circular form.

00The fourth book deals with the circle in its relations to inscribed and circumscribed triangles, quadrilaterals and regular polygons.

00Taking the circumference as intermediate between the perimeters of the inscribed and the circumscribed regular n-gons, he showed that, the radius of the circle being given and the perimeter of some particular circumscribed regular polygon obtainable, the perimeter of the circumscribed regular polygon of double the number of sides could be calculated; that the like was true of the inscribed polygons; and that consequently a means was thus afforded of approximating to the circumference of the circle.

00The latter, as we know, calculated the perimeters of successive polygons, passing from one polygon to another of double the number of sides; in a similar manner Gregory calculated the areas.

00In book v., after an interesting preface concerning regular polygons, and containing remarks upon the hexagonal form of the cells of honeycombs, Pappus addresses himself to the comparison of the areas of different plane figures which have all the same perimeter (following Zenodorus's treatise on this subject), and of the volumes of different solid figures which have all the same superficial area, and, lastly, a comparison of the five regular solids of Plato.

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.

00As regards the funicular diagram, let LM be the line on which the pairs of corresponding sides of the two polygons meet, and through it draw any two planes w, w.

00and the corresponding polygons in the other figure by the same letters; a line joining two points A, B in one figure will then correspond to the side common to the two polygons A, B in the other.

00The stresses produced by extraneous forces in a simple frame can be found by considering the equilibrium of the various joints in a proper succession; and if the graphical method be employed the various polygons of force can be combined into a single force-diagram.

00Relations between Polygons of Loads and of Resistances.In a structure in which each piece is supported at two joints only, the well-known laws of statics show that the directions of the gross load on each piece and of the two resistances by which it is supported must lie in one plane, must either be parallel or meet in one point, and must bear to each other, if not parallel, the proportions of the sides of a triangle respectively parallel to their directions, and, if parallel, such proportions that each of the three forces shall be proportional to the distance between the other two,all the three distances being measured along one direction.

00By constructing several partial polygons, and computing the relations between the loads and resistances which are determined by the application of that theorem to each of them, with the aid, if necessary, of Moseleys principle of the least resistance, the whole of the relations amongst the loads and resistances may be found.

00It must be remembered that these are all directed quantitie~, and that their respective sums are to be taken by drawing vector polygons.

00In drawing these polygons the magnitude of the vector of the type Wr is the product Wr, and the direction of the vector is from the shaft outwards towards the weight W, parallel to the radius r.

00" Regular polyhedra " are such as have their faces all equal regular polygons, and all their solid angles equal; the term is usually restricted to the five forms in which the centre is singly enclosed, viz.

00These have faces which are all regular polygons, but not all of the same kind, while all their solid angles are equal.

00These figures are often termed " semi-regular solids," but it is more convenient to restrict this term to solids having all their angles, edges and faces equal, the latter, however, not being regular polygons.

00- These solids have all their faces equal regular polygons, and the angles at the vertices all equal.

00They bear a relation to the Platonic solids similar to the relation of " star polygons " to ordinary regular polygons, inasmuch as the centre is multiply enclosed in the former and singly in the latter.

00- These solids are characterized by having all their angles equal and all their faces regular polygons, which are not all of the same species.

00Although this term is frequently given to the Archimedean solids, yet it is a convenient denotation for solids which have all their angles, faces, and edges equal, the faces not being regular polygons.

00It is possible to attempt to remove sliver polygons automatically.

00Drawing polygons Use the polygon tool to click points representing the vertices of the required polygon.

00We'll also be making sure all the polygons have four vertices (called quads).

00Characters are realistic and not blocky sets of polygons.

00Character design is okay, the Dreamcast wasn't pushing a lot of polygons in this game and there were hardly any cut-scenes to speak of.

00Engine: Capable of drawing 120,000 polygons per second @ 30 million pixels per second.

00She's a bit ornery in comparison and not as physically capable, but she's my puppy and I wouldn't trade her for all the polygons in the world.

00Even though these are virtual dogs composed of lines of code and polygons, they still tug at your heart and make onlookers coo and whimper at their cuteness.

00However, because the polygons are smaller, the overall look is much less blocky.

00The days of simple entertainment seem to be gone, swallowed by pixels, polygons and processing power.

00

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.