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THE AUTHOR’S PROPOSITION ON FIGURE III.

A NEW AND UNIVERSAL COMPASS, FOR DESCRIBING, BY THE ORDER OF PYRAMIDS AND RECTILINEAR FIGURES, ANY PLANE CURVILINEAR FIGURES WHATSOEVER, WHICH CORRESPOND TO THE ORDER OF THE RECTILINEAR FIGURES THEMSELVES.

Declaration of the same Third Figure.

Decorative drop cap 'H' featuring intricate foliage and scrollwork.These are the parts of this excellent Compass. In the East is a Leg; first extending from North to South; whose Southern part is of three points, by which the Pyramid will strike; whose Base to the North is an equilateral rectilinear triangle. This, however, is fixed, or rotates around the fixed Leg. If quadrilateral and other multilaterate Figures are moved, they cannot be described by this Compass in one stroke, for the side of the Pyramid will have to be subtended to the side of the proposed Figure: if, however, it is fixed, many Pyramids will be necessary for the construction of the lines of the Figure. The remaining framework relates to the motion or stability of the machine. Its Northern Arm, drawn parallel to the Southern line from East to West, and 20 parts long according to our measures, rotates around the fixed Leg in that part which is distant from the points by 12 parts. In this, two Parallel Rulers move squarely, in whose middle moves a small oblong square arm, at whose Eastern extremity the center of a small wheel is inserted: for the Wheel rotates around each side of the Pyramid, so that the mobile point (which is in the third arm from the North) may be moved toward and away from the East. An arc, Turkish-style, is placed upon it, so that with one hand applied to it, and the other to the fixed Leg, the Figure is described; which is made larger or smaller as the mobile point is moved toward the Pyramid or away from it. However, it must be noted that the middle of the arc is always joined to the small arm.

Addition.

BUT the Pyramid exposed above should always be separable: namely, so that it can be both removed and moved to that fixed Leg whenever the need arises. Its hole, which appears in its base, should be square, and not otherwise; just as that square part of the Leg, which is inserted into the Pyramid, must also be square. But there are also other Pyramids; besides this one, which we see as triangular; very many must be kept, both quadrilateral and pentagonal or hexagonal; according to how it pleases each person to construct multilaterate Figures. For this instrument cannot be called a Compass, except insofar as it describes a single Figure for us in a single stroke only (as we are accustomed to with a Compass): which will certainly happen, according to the proposed Pyramid. But one must also note those holes which are visible to us in the fixed leg above the Pyramid, to the North, and they have this use: namely, to admit a nail, extended from the Pyramid, for the sake of lifting it; if, when a shorter Figure is being described, the point of the immovable Leg, due to the thinness of the Pyramid itself, could not be deeply inserted into it.

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