The stranger, Isaac Beeckman, principal of the college of Dort, offered to do so into Latin, if the inquirer would bring him a solution of the problem, - for the advertisement was one of those challenges which the mathematicians of the age were accustomed to throw down to all corners, daring them to discover a geometrical mystery known as they fancied to themselves alone.
Investigation of the writings of Indian mathematicians has exhibited a fundamental distinction between the Greek and Indian mind, the former being pre-eminently geometrical and speculative, the latter arithmetical and mainly practical.
But in the great Sala dell' Asse (or della Torre) abundant traces of Leonardo's own hand were found, in the shape of a decoration of intricate geometrical knot or plait work .combined with natural leafage; the abstract puzzle-pattern, of a kind in which Leonardo took peculiar pleasure, intermingling in cunning play and contrast with a pattern of living boughs and leaves exquisitely drawn in free and vital growth.
Besant, Geometrical Conic Sections; C. Smith, Geometrical Conics; W.
Thus the number lox in the arithmetical column corresponds to 10 8 (1.0001) x in the geometrical column; the intermediate numbers being obtained by interpolation.
The radius of the pitch-circle of a wheel is called the geometrical radius; a circle touching the ends of the teeth is called the addendum circle, and its radius the real radius; the difference between these radii, being the projection of the teeth beyond the pitch-surface, is called the addendum.
In his youth he went to the continent and taught mathematics at Paris, where he published or edited, between the years 1612 and 1619, various geometrical and algebraical tracts, which are conspicuous for their ingenuity and elegance.
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.
Metrical relations between the axes, eccentricity, distance between the foci, and between these quantities and the co-ordinates of points on the curve (referred to the axes and the centre), and focal distances are readily obtained by the methods of geometrical conics or analytically.
In such experiments the narrowness of the zones renders necessary a pretty close approximation to the geometrical conditions.