Geometrical Lectures: Explaining the Generation, Nature and Properties of Curve Lines

S. Austen, 1735 - Curves - 309 pages

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Page 10 - Flux, inasmuch as it can be divided some how or other. And like as the Quantity of a Line consists of but one Length following the Motion; so the Quantity of Time pursues but one Succession stretched out as it were in Length, which the Length of the Space moved over shews and determines. We therefore shall always express Time by a right Line...
Page 4 - Proportionably to the respective Parts of an equal Motion, or to the Parts of Spaces moved through with an equal Motion; it may therefore be very aptly represented to our Minds, by any Magnitude alike in all its Parts; and especially by the most simple ones, such as a strait or circular Line; between which and Time there happens to be much Likeness and Analogy.
Page 278 - DIRECTIONS FOR THE Profitable Reading of the Holy Scriptures^ TOGETHER With fome Obfervations for the Confirming their Divine Authority, and HJuilrating the Iiiiiculties thereof.
Page 277 - With particular Accounts of the different Appearances of the Heavens in different Countries; the Seafons of the Year over all the Globe; the Tides of the Sea; Bays, Capes, Iflands, Rocks, Sand-Banks, and Shelves. The State of the Atmofphere ; the Nature of Exhalations; Winds, Storms, Tornados...
Page 20 - ... endowed with one dimension only; for we imagine it to be made up, as it were, either of the simple addition of rising Moments, or of the continual flux of one Moment, and for that reason ascribe only length to it, and determine its quantity by the length of the line passed over : As a line, I say, is looked upon to be the trace of a point moving forward, being in some sort divisible by a point, and may be divided by Motion one way, viz. as to length ; so Time may be conceived as the trace of...
Page 10 - ... or circular line, between which and time there happens to be much likeness and analogy. For as time consists of parts altogether similar, it is reasonable to consider it as a quantity endowed with one dimension only; for we imagine it to be made up, as it were, either of the simple addition of rising moments or of the continual flux of one moment and for that reason ascribe only length to it and determine its quantity by the length of the line passed over. As a line, I say, is looked upon to...
Page 3 - Offices. For, in like Manner as we first of all measure a Space by some Magnitude, and declare it is so much; and afterwards by Means of this Space, compute other Magnitudes correspondent with it: So we first assume Time from some Motion, and afterwards judge thence of other Motions, which in Reality is no more than comparing some Motions with others, by the Assistance of Time; just as we investigate the Ratios of Magnitudes by the help of some Space.
Page 79 - In other words, the ratio of the velocities is equal to the ratio of the intercepts divided by the ratio of the applied lines.