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The application of the rectilinear system consists in the use, as a basis of the drawing, of such a series of triangles as shall at once show the exact relation of the points of definition or expression to each other; but the successful application of this depends much on the assistance of the trained eye and hand of a master watching every step we make.
When mechanics had reached the point to which Galileo brought it when the simple laws of force had been disentangled from the friction and atmospheric resistance by which all their earthly manifestations are disguised when progressing knowledge of physics had given a due insight into these disturbing causes when, by an effort of abstraction, it was perceived that all motion would be uniform and rectilinear unless interfered with by external forces and when the various consequences of this perception had been worked out; then it became possible, by the union of geometry and mechanics, to initiate physical astronomy.
The two distinct types of lenses are the "rapid rectilinear" and the "anastigmatic," which names refer to their optical properties in distributing the light.
Their calculations on the eccentricity of the moon prove that they had a rectilinear trigonometry and tables of chords. They understood spherical trigonometry, and determined the motions of the sun and moon, involving an accurate definition of the year, and a method of predicting eclipses.
Sardinia furnishes some fine examples of rectilinear work, while the best of the curved designs are found in Malta, where elaborate conventional and even naturalistic patterns are traced out with wonderful freedom and steadiness of hand. The pottery of the megalithic area is not all alike; it would be surprising if it were.
Unable to slip back in triumph to my studies I elected to stroll spiritlessly into the billiard room where certainly I had no business. There was no one there either, and I felt very lost and desolate under its high ceiling, all alone with the massive English billiard table which seemed, in heavy, rectilinear silence, to disapprove of that small boy's intrusion.
There are however two simple sets of routes which are of vital importance. One is a set of momental routes and the other of vagrant routes. Both sets can be classed together as straight routes. We proceed to define them without any reference to the definitions of volumes and surfaces. The two types of straight routes will be called rectilinear routes and stations.
Besides, no element is divided into things compounded of itself; indeed there is a dissolution of all other things into the elements. Now a triangle is divided into no circumference, but two diameters cut a circle into four triangles; therefore a rectilinear figure is before a circular, and has more of the nature of an element.
It would become merged in this spiral if the number of radii were infinite, for this would reduce the length of the rectilinear elements indefinitely and change this polygonal line into a curve.
It has passed by the side; but sufficiently near to be retained by the lunar attraction. The rectilinear movement has thus become changed into a circular motion of extreme velocity, and it is now pursuing an elliptical orbit round the moon, of which it has become a true satellite.
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