# Mensuration Sentence Examples

- This applies not only to the geometrical principles but also to the arithmetical principles, and it is therefore of importance, in the earlier stages, to keep geometry,
**mensuration**and arithmetic in close association with one another;**mensuration**forming, in fact, the link between arithmetic and geometry. - All exact relations pertaining to the
**mensuration**of the circle involve the ratio of the circumference to the diameter. - General aspects of the subject are considered under
**Mensuration**; Vector Analysis; Infinitesimal Calculus. - This use of formulae for dealing with numbers, which express magnitudes in terms of units, constitutes the broad difference between
**mensuration**and ordinary geometry, which knows nothing of units. **Mensuration**involves the use of geometrical theorems, but it is not concerned with problems of geometrical construction.**Mensuration**of the Circle.- For the subjects under this heading see the articles CONIC SECTIONS; CIRCLE; CURVE; GEOMETRICAL CONTINUITY; GEOMETRY, Axioms of; GEOMETRY, Euclidean; GEOMETRY, Projective; GEOMETRY, Analytical; GEOMETRY, Line; KNOTS, MATHEMATICAL THEORY OF;
**MENSURATION**; MODELS; PROJECTION; Surface; Trigonometry. - The term "
**mensuration**" is therefore ordinarily restricted to the measurement of areas and volumes, and of certain simple curved lengths, such as the circumference of a circle. - (ii) The very earliest stages of
**mensuration**should be directly associated with simple arithmetical processes. - The next stage is geometrical
**mensuration**, where geometrical methods are applied to determine the areas of plane rectilinear figures and the volumes of solids with plane faces. - The third stage is analytical
**mensuration**, the essential feature of which is that account is taken of the manner in which a figure is generated. **Mensuration**Of Specific Figures (Geometrical) 22.- - The
**mensuration**of the circle is founded on the property that the areas of different circles are proportional to the squares on their diameters. - - For elementary
**mensuration**the ellipse is to be regarded as obtained by projection of the circle, and the ellipsoid by projection of the sphere. - 37 The
**mensuration**of earthwork involves consideration of quadrilaterals whose dimensions are given by special data, and of prismoids whose sections are D such quadrilaterals. - [[
**Mensuration**Of Graphs 38.]] (A) Preliminary. - To illustrate the importance of the
**mensuration**of graphs, suppose that we require the average value of u with regard to x. - The processes which have to be performed in the
**mensuration**of figures of this kind are in effect processes of integration; the distinction between**mensuration**and integration lies in the different natures of the data. - The province of
**mensuration**is to express the final result of such an elimination in terms of the data, without the necessity of going through the intermediate processes. - In elementary geometry we deal with lines and curves, while in
**mensuration**we deal with areas bounded by these lines or curves. - The circle, for instance, is regarded geometrically as a line described in a particular way, while from the point of view of
**mensuration**it is a figure of a particular shape. - Similarly, analytical plane geometry deals with the curve described by a point moving in a particular way, while analytical plane
**mensuration**deals with the figure generated by an ordinate moving so that its length varies in a particular manner depending on its position. - In the same way, in the case of a figure in three dimensions, analytical geometry is concerned with the form of the surface, while analytical
**mensuration**is concerned with the figure as a whole. - (B)
**Mensuration**of Graphs of Algebraical Functions. - (C)
**Mensuration**of Graphs Generally. - The relation between the inaccuracy of the data and the additional inaccuracy due to substitution of another figure is similar to the relation between the inaccuracies in
**mensuration**of a figure which is supposed to be of a given form (§ 20). - In the case of a trapezette, for instance, the data are the magnitudes of certain ordinates; the problem of interpolation is to determine the values of intermediate ordinates, while that of
**mensuration**is to determine the area of the figure of which these are the ordinates. - - FOr applications of the prismoidal formula, see Alfred Lodge,
**Mensuration**for Senior Students (1895). - Other works on elementary
**mensuration**are G. - Chivers, Elementary
**Mensuration**(1904); R. - Edwards, Elementary Plane and Solid
**Mensuration**(1902); William H. - Pierpoint's
**Mensuration**Formulae (1902) is a handy collection. - C. Turner, Graphics applied to Arithmetic,
**Mensuration**and Statics (1907). - The
**mensuration**of the cube, and its relations to other geometrical solids are treated in the article Polyhedron; in the same article are treated the Archimedean solids, the truncated and snubcube; reference should be made to the article Crystallography for its significance as a crystal form. - From these results the
**mensuration**of any figure bounded by circular arcs and straight lines can be determined, e.g. - Philosophy, grammar, the history and theory of language, rhetoric, law, arithmetic, astronomy, geometry,
**mensuration**, agriculture, naval tactics, were all represented. - Such knowledge, he here maintains, is really
**mensuration**of pleasures and pains, whereby the wise man avoids those mistaken under-estimates of future feelings in comparison with present which we commonly call " yielding to fear or desire." - Besides agriculture, the course of instruction at the college includes chemistry, natural and mechanical philosophy, natural history,
**mensuration**, surveying and drawing, and other subjects of practical importance to the farmer, proficiency in which is tested by means of sessional examinations. - In actual practice, surds mainly arise out of
**mensuration**; and we can then give an exact definition by graphical methods. - While
**mensuration**is concerned with the representation of geometrical magnitudes by numbers, graphics is concerned with the representation of numerical quantities by geometrical figures, and particularly by lengths. - There are also cases in which graphics and
**mensuration**are used jointly; a variable numerical quantity is represented by a graph, and the principles of**mensuration**are then applied to determine related numerical quantities. - In 1764 he published his first work, The Schoolmaster's Guide, or a Complete System of Practical Arithmetic, which in 1770 was followed by his Treatise on
**Mensuration**both in Theory and Practice. - The statement that, if the adjacent sides of a rectangle are represented numerically by 3 and 4, the diagonal is represented by 5, is as much a matter of
**mensuration**as the statement that the area is represented by 12. **Mensuration**is not concerned with the first of these two processes, which forms part of the art of measurement, but only with the second.- It is also convenient to regard as coming under
**mensuration**the consideration of certain derived magnitudes, such as the moment of a plane figure with regard to a straight line in its plane, the calculation of w]iich involves formulae which are closely related to formulae for determining areas and volumes. - If these are included in the description "
**mensuration**," the subject thus consists of two heterogeneous portions - elementary**mensuration**, comprising methods and results, and advanced**mensuration**, comprising certain results intended for practical application. **Mensuration**, then, is mainly concerned with quadratureformulae and cubature formulae, and, to a not very clearly defined extent, with the methods of obtaining such formulae; a quadrature-formula being a formula for calculating the numerical representation of an area, and a cubature-formula being a formula for calculating the numerical representation of a volume, in terms, in each case, of the numerical representations of particular data which determine the area or the volume.- In developing a system of
**mensuration-formulae**the importance of this latter group of cases must not be overlooked. - As a result of the importance both of the formulae obtained by elementary methods and of those which have involved the previous use of analysis, there is a tendency to dissociate the former, like the latter, from the methods by which they have been obtained, and to regard
**mensuration**as consisting of those mathematical formulae which are concerned with the measurement of geometrical magnitudes (including lengths), or, in a slightly wider sense, as being the art of applying these formulae to specific cases. - On the other hand,
**mensuration**, in its practical aspect, is of importance for giving reality to the formulae themselves and to the principles on which they are based. - The main object to be aimed at, therefore, in the study of elementary
**mensuration**, is that the student should realize the possibility of the numerical expression of areas and volumes. - - The methods of
**mensuration**fall for the most part under one or other of three main heads, viz. - Arithmetical
**mensuration**, geometrical**mensuration**, and analytical**mensuration**. - The most elementary stage is arithmetical
**mensuration**, which comprises the measurement of the areas of rectangles and parallelepipeds. - This may be introduced very early; square tablets being used for the
**mensuration**of areas, and cubical blocks for the**mensuration**of volumes. - The measure of the area of a rectangle is thus presented as the product of the measures of the sides, and arithmetic and
**mensuration**are developed concurrently. - Lambert, Computation and
**Mensuration**(1907).