Also, Tables of Weights, Areas andCircumferences of Circles, and other Matter calculated to Benefit the Trade.
Therefore, as the circumferences of the two phials were one foot and two feet respectively and the cubes of one and two added together make nine, what we have to find is two other numbers whose cubes added together make nine.
Now all these circumferences have for a common tangent the straight line BN; namely the same line which is drawn as a tangent from the point B to the circumference SNR which we considered first.
For it is easy to see that all the other circumferences will touch the same BN, from B up to the point of contact N, which is the same point where AN falls perpendicularly on BN.
It seems all circles are not similar figures, there not being the same proportion betwixt all circumferences & their diameters.
Archimedes's proposition about squaring the circle has nothing to do with circumferences containing less than 96 points; & if the circumference contain 96 points it may be apply'd, but nothing will follow against indivisibles.
Attached to it on the outside were thirteen forts, whose united circumferences measured ten furlongs.
Now, at this wall without were erected thirteen places to keep garrison in, whose circumferences put together amounted to ten stadia.
A C is the line joining the centres, and D F the common tangent of the circles at e; which is at right angles with A C; and so are the circumferences of the two circles at the point e.
Two circumferences having the same radius are equal.
The principal argument, on which the distinction is founded, may be combatted by observing that the circumferences which may be traced or represented, are only forms of the idea, not the idea itself.
Then there are not two circumferences in the purely ideal order, but one only, whose properties we know under different conceptions, and express in various ways.
As a consequence of this we get If the circumferences of the two circles have three points in common they coincide.
But two circles which have a common centre, and whose circumferences have a point in common, coincide.
This enables the grinding of such short cones as the circumferences of bevelled cutters, chamfers, &c.
The diameter A being equal to that of B their circumferences will be equal, and the angular and velocity ratios will therefore be equal.
In both the chucks thus far described, the construction has been arranged to close the splits and thus grip the circumferences of cylindrical bodies, but in Fig.
First, the top has a larger circle of rotation than has the bottom, and, therefore, its cutting speed is greater, to an amount equal to the difference between the circumferences of the thread at the top and at the bottom.
Euclid dismisses all this with the simple theorem, "In equal circles equal circumferences are subtended by equal straight lines.
The lateral area of a frustum of a cone of revolution is equal to half the sum of the circumferences of its bases multiplied by the slant height.
Two circumferences have the same ratio as their radii.
Finally, let us trace points, o and c, as centers of arcs of circles having respectively for radii the distance between the centers of the circumferences just mentioned and the eccentricity of the expansion slide-valve.
In the majority of cases it is not until the second year or thereabouts that the two circumferences become equal.
These two circumferences are to be considered together, according to Godin, as expressing the relation between the organs of respiration and the muscular mass.
The proportionality of the circumferences of circles to their radii must be inferred directly from the proportionality of the perimeters of regular polygons, of the same number of sides, to their apothems.
The circumferences of circles are to each other as their radii.
When people begin to make so very few words serve their purpose it shows that their circumferences have intersected--no mere tangents now.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "circumferences" in a variety of sentences. We hope that you will now be able to make sentences using this word.
