NBoOOk VIII. Mechanic Powers. 171lines of all the points deſcribed by the motion of any circle, may

be determin' d howwfOver cis moved on one or another; whichmay be of great uſe in Aſtronomy.

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The Spiral motion of Sphæres ma) be explicated, to wit,when a Sphære is moved Sy a motion mit„ Right andCircular, or f tio Circular ones.

Fig. 1 7.P in che firſt place, let the Sphære BC be moved by5 its Centre A through the right line A H, and at theſame timè turn it about the axis B C; moreover every point,except the Poles B, C, deſcribes Spiral lines, as if they were

Spires, ar wreaths, about divers Cylinders, about the greater

Cylinder, truly the ſpire Which it deſcribes is from the point

For G, but about the leſſer, which is deſcribed from the point,

next to the pole C or B. But if it be turned about the Axis

FEG, or any other oblique, it will be another divers mixt mo-

tion in divers points, whoſe lines may eaſily be found by the

foreſaid doctrine. ö

In the ſecond place, let the point G be moved through thearch GC, and at the ſame time underſtand it to move about

the Axis B C, it will be a Sphærical Spiral motion mixt of a

double circular. N 5

Thirdly, let the ſame point& be moved through the rightlight line G C, while tis moved alſo about the Axis B C; themotion will be conicaly Spiral, mixt of Right and Circular.

Beſides the Sphcerie Spiral motion, there may be made anothermotion Conoid Spiral, to wit, if a Conoid be turn'd about one, orabout the other Axis, while its point is ſomewhat movedthrough a right line; and tis of a threefold kind, viz. either

Eiliptic, or Parabolic, Or Hyberbolic, as appears by Geometiy, and

from the Mechanic deſcription of thoſe figures. N

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