Indeed we may consider the engine as the material and mechanical representative of analysis, and that our actual working powers in this department of human study will be enabled more effectually than heretofore to keep pace with our theoretical knowledge of its principles and laws, through the complete control which the engine gives us over the executive manipulation of algebraical and numerical symbols.
Most convincing to me of the spiritual relations between mathematics and music, is my own very personal experience. Composing in an amateurish way, I get exactly the same elevation from a prelude that has come to me at the piano, as I do from a new idea that has come to me in mathematics.
The design of this Memoir is to deduce strictly from a few principles, obtained chiefly by experiment, the rationale of those electrical phenomena which are produced by the mutual contact of two or more bodies, and which have been termed galvanic; its aim is attained if by means of it the variety of facts be presented as unity to the mind.
Mathematicks therefore is a Science which teaches or contemplates whatever is capable of Measure or Number as such. When it relates to Number, it is called Arithmetick; but when to measure, as Length, Breadth, Depth, Degrees of Velocity in Motion, Intenseness or Remissness of Sounds, Augmentation or Diminution of Quality, 6tc. it is called Geometry.
The Ancients, having taken into consideration the rigorous construction of the human body, elaborated all their works, as especially their holy temples, according to these proportions; for they found here the two principal figures without which no project is possible: the perfection of the circle, the principle of all regular bodies, and the equilateral square.
[Science] advances by leaps; and the impulse for each leap is either some new observational resource, or some novel way of reasoning about the observations. Such novel way of reasoning might, perhaps, be considered as a new observation means, since it draws attention to reactions between facts which would previously have been passed by unperceived.
The heaven is spherical in shape, and moves as a sphere; the earth too is sensibly spherical in shape, when taken as a whole; in position it lies in the middle of the heavens very much like its center; in size and distance it has the ratio of a point to the sphere of the fixed stars; and it has no motion from place to place.
The more progress physical sciences makes, the more they tend to enter the domain of mathematics, which is a kind of center to which they all converge. We may even judge of the degree of perfection to which a science has arrived by the facility with which it may be submitted to calculation.