In mathematics, he was the first to draw up a methodical treatment of mechanics with the aid of geometry; he first distinguished harmonic progression from arithmetical and geometrical progressions.
Maclaurin's object was to found the doctrine of fluxions on geometrical demonstration, and thus to answer all objections to its method as being founded on false reasoning and full of mystery.
By geometrical consideration it can be shown that the angle subtended by p, as seen from F, must be inversely as the square of its distance r.
This, and the inclination of the orbit being given, we have all the geometrical data necessary to compute the coordinates of the planet itself.
The windows in the outer walls are filled with pierced stone screens of geometrical design.
The most beautiful portion of the mosque, however, still exists in the prayer chamber of Hakim, where are to be found the earliest examples of the cusped arch and the origin of many of the geometrical patterns in stucco at the Alhambra.
The "axioms" of geometry are the fixed conditions which occur in the hypotheses of the geometrical propositions.
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.
Among the contents of this book we simply mention a trigonometrical chapter, in which the words sinus versus arcus occur, the approximate extraction of cube roots shown more at large than in the Liber abaci, and a very curious problem, which nobody would search for in a geometrical work, viz.
He not only freed it from all trammels of geometrical construction, but by the introduction of the symbol b gave it the efficacy of a new calculus.
His purely abstract mode of regarding functions, apart from any mechanical or geometrical considerations, led the way to a new and sharply characterized development of the higher analysis in the hands of A.
His geometrical discoveries are of great value, his Die freie Perspective (1759-1774) being a work of great merit.
LORENZO MASCHERONI (1750-1800), Italian geometer, was professor of mathematics at the university of Pavia, and published a variety of mathematical works, the best known of which is his Geometria del compasso (Pavia, 1797), a collection of geometrical constructions in which the use of the circle alone is postulated.
The main work of Descartes, so far as algebra was concerned, was the establishment of a relation between arithmetical and geometrical measurement.
The association of algebra with arithmetic on the one hand, and with geometry on the other, presents difficulties, in that geometrical measurement is based essentially on the idea of continuity, while arithmetical measurement is based essentially on the idea of discontinuity; both ideas being equally matters of intuition.
The difficulty first arises in elementary mensuration, where it is partly met by associating arithmetical and geometrical measurement with the cardinal and the ordinal aspects of number respectively (see Arithmetic).
I could not follow with my eyes the geometrical figures drawn on the blackboard, and my only means of getting a clear idea of them was to make them on a cushion with straight and curved wires, which had bent and pointed ends.
The geometrical diagrams were particularly vexing because I could not see the relation of the different parts to one another, even on the cushion.
"The third, I said the third!" cried the prince abruptly, pushing the letter away, and leaning his elbows on the table he drew toward him the exercise book containing geometrical figures.
Only when we have admitted the conception of the infinitely small, and the resulting geometrical progression with a common ratio of one tenth, and have found the sum of this progression to infinity, do we reach a solution of the problem.