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

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A M B apply'd Arch Archimedes arithmetical Mean Centre Circle circular Sectors conceived Cone conical Curve AMB Curve FBF Curve Superficies cutting Degree of Velocity demonstrated described draw the right drawing any right drawn equal Equation evident fall fame Manner fame Order fame thing Figure given in Position greater Hence Hyperbola Hyperbolick indefinitely intercepted intersecting joyn let the Curve let the Line let the right Line BC Magnitudes manifest moveable Number Ordinates Parabola Paraboloid parallel Motion parallel to D B Parallelogram pendicular perpendicular Plane Point G Proportion Quantity rallel Rectangle right Angle right Line AC Roots Segment Solid Space moved Subtense suppose Tangent ther thro tion touch the Curve transverse Motion Triangle Whence Wherefore

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Page 18 - 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 12 - 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 30 - ... 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 3 - Common Sense, therefore allows Time to partake of Quantity, as the Measure of the Continuance of Things in their Being. But perhaps you may ask, whether Time was not before the World was created? And if Time does not flow in the Extramundane Space, where nothing is: A mere Vacuum? I answer, that since there was Space before the World was created, and that there now is an Extramundane, infinite Space, (where God is present;) inasmuch as there might have been of old, and now may be, such, and so many...

Page 18 - ... 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 11 - 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 87 - In other words, the ratio of the velocities is equal to the ratio of the intercepts divided by the ratio of the applied lines.