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In pure air you cannot see the beam, but in smoky air you can, because the light, which passes unseen through the air, is scattered and revealed by the smoke particles, among which the beam pursues a straight course. The following instructive experiment depends on the rectilineal propagation of light.
I can imagine but one way of making it seem possible, namely, that this round square or rectilineal curve this honest Jesuit, I mean had confined his conception of idolatry to the worship of false gods; whereas his saints are genuine godlings, and his 'Magna Mater' a goddess in her own right; and that thus he overlooked the meaning of the word. Ib. p. 254.
They assured themselves of the rectilineal propagation of light, and that the angle of incidence was equal to the angle of reflection.
To Intuition it is opposed, for this takes in those principles which cannot be proved by reasoning, while Practical Wisdom is concerned with the ultimate particular fact which cannot be realised by Knowledge but by Sense; I do not mean one of the five senses, but the same by which we take in the mathematical fact, that no rectilineal figure can be contained by less than three lines, i.e. that a triangle is the ultimate figure, because here also is a stopping point.
It announced: That on December 13th, at 2 o'clock in the morning, the Projectile shot from Stony Hill had been perceived by Professor Belfast and his assistants; that, deflected a little from its course by some unknown cause, it had not reached its mark, though it had approached near enough to be affected by the Lunar attraction; and that, its rectilineal motion having become circular, it should henceforth continue to describe a regular orbit around the Moon, of which in fact it had become the Satellite.
But our thought finds it very difficult to sustain such an effort long. It is partial to rectilineal deduction, actual becoming horrifies it. It desires immediately to find "things" sharply determined and very clear. That is why immediately a tangent is constructed, it follows its movement in a straight line to infinity. Thus are produced limit-concepts, the ultimate terms, the atoms of language.
The most elementary case appears in Eucl. I. 44, 45, where it is shown how to apply to a given straight line as base a parallelogram with one angle equal to a given angle and equal in area to any given rectilineal figure; this construction is the geometrical equivalent of arithmetical division.
Another problem solved by the Pythagoreans was that of drawing a rectilineal figure which shall be equal in area to one given rectilineal figure and similar to another. Plutarch mentions a doubt whether it was this problem or the theorem of Eucl. I. 47 on the strength of which Pythagoras was said to have sacrificed an ox.
To deduce the laws of the heavenly motions, we require not only to know the law of a rectilineal and that of a gravitative force, but the existence of both these forces in the celestial regions, and even their relative amount. We shall hereafter have occasion to return to this distinction, and to dwell on it at such length as dispenses with the necessity of further insisting on it here.
Yet the law of the parabolic motion would be resolvable into the very same simple laws into which that of the elliptical motion is revolved, namely, the law of the permanence of rectilineal motion, and the law of gravitation.
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