Geometry: dividing lines and finding an arc's radius
Constructions to partition segments, locate an arc's center, and raise a perpendicular
The central constructions divide a line into equal parts by erecting equal perpendiculars at its endpoints (f a b e above and below, and m c d n) and joining corresponding points along them. A further figure finds the radius of curvature of an arc a b, locating its center m by intersecting arcs at f and g and raising perpendiculars at c and e. A last construction raises a perpendicular f over a chosen point e of segment a b, and a faint freehand variant of the figure appears near the outer edge.
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Dividing lines with paired perpendiculars
Perpendiculars are erected above and below each line's endpoints (f b and a e over line a b; m c and d n over line c d). Joining points set at equal distances along these perpendiculars partitions the original segment into equal parts.
Faint variant sketch at the edge
Near the outer edge of the sheet a smaller, faint freehand sketch repeats the central construction. It bears no lettering of its own.
Radius of curvature of arc a b
With a fixed compass opening, arcs are traced from each endpoint and then from point d where they meet the larger arc, giving intersections f and g. Perpendiculars raised at c and e meet at m, which marks the radius of the arc's curvature.
Raising a perpendicular over point e
On segment a b the compass is set once at each of two points c and d equidistant from a chosen point e. The two arcs meet at f, and line f e is the perpendicular erected over point e.