Geometric constructions for large arcs, and a furnace varnish
Proportional division of a triangle, an irregular heptagon in a circle, and a metal-paste varnish
A heading on the 'varnish of the furnace' prescribes a paste of Mercury with Jove and Venus that is to be corrected continually with the template until Mercury separates entirely from the other two metals. The rest of the leaf is geometry: a diagram whose parallelogram side is divided into 128 parts with added triangles, a triangle divided into fifteen parts, and a construction that draws part of a circle's arc between two converging lines a c and b d using equal circles, the compass and the line p r. A closing note observes that in a circle of unequal sides the angles always fall between sides equidistant from the centre.
On this page
Varnish for the furnace: a paste of three metals
Varnish of the furnace: Mercury with Jove and Venus, having made the paste of it, is to be corrected continually with the template until Mercury separates entirely from Jove and Venus.
Arc drawn between two converging lines
Given the converging lines a c and b d, produce the line a b between their ends and divide it into 4 equal parts. Make two equal circles on the equal angles c a b and a b d occupying two quarters of a b; take the curve n m with the compass and carry it to m o; then draw the line p r through the intersections of those quarters with the circle.
Proportional division of a parallelogram with triangles
Let a n o p q be needles; f g, the base of the triangle, goes 127 times into the axis f q. Divide the parallelogram side h f–a q into 128 equal parts and add the triangles h S and f g q; the bases each equal one of the 128 degrees, so that S g is the 'real', a q the 'resultant', and a q K the 'son'.
Angles of an irregular heptagon in a circle
Here, in a circle of unequal sides, the angles are always set between the sides equidistant from the centre of the circle.