Using this method, an arc of a circle is drawn with a radius that is some multiple of the diagonal's length. The length of this radius is established at the designer's discretion (Bouguer 1746:45), and its length reflects how much "fullness" is desired in the final shape of the curve. For La Belle's offsets along the after floor diagonal, I reconstructed a radius 3.5 times the diagonal fa's length (Figure 41a). A perpendicular is then extended from point a to the arc, and this vertical distance is then subdivided equally with horizontal lines into the number of offsets desired. The intersections of these horizontals with the arc provide offset distances for subdividing length fa. Plotting these offsets out along the ship's length transforms the circular arc used in the geometric offset diagram into part of an elliptical curve.

The oldest example of this geometric method of establishing offsets for a curve dates back to the third century B.C. In 1979 Lothar Haselberger discovered a diagram based on the same principles etched onto one of the unfinished walls of the Temple of Apollo at Didyma in present-day Turkey (Haselberger 1985:130, 131). In this diagram, a circle with an approximately 3.2-m radius was used to generate offset measurements for the slight profile curvature, or entasis, of the 18-m-long shafts of the temple's columns (Haselberger 1985:131).

In Figure 41a the offset sequence resulting from the convexity of arcs method is compared to the base sequence of the equilateral triangle generated by the arithmetic method reconstructed for La Belle. The two offset sequences are similar to each other, deviating the most at the offsets for VIIIID and XIID. The arithmetic sequence is a better fit for the reconstructed shape of the archaeological hull remains, but the convexity of arcs method has much stronger documentary parallels. Regardless of whether or not it can be established with absolute certainty which of these methods was used in La Belle's design, both provide a similar offset sequence that subdivides the full length of La Belle's after floor diagonal and predicts the same value for the offset at frame XVD.

Of course, there is no way to prove that La Belle's frame XVD originally intersected the diagonal at this predicted guide point. However, the 1684 draft of the Profond provides confirmation that this same sequence was actually used in French shipbuilding. When the triangle reconstructed for La Belle is superimposed on after floor diagonal in the body plan of the Profond, it corresponds closely with the intersections of the frames (Figure 42). Most importantly, the guide point predicted for XVD, which has no archaeological confirmation, corresponds exactly with the upper endpoint of the Profond's floor diagonal. Recall that La Belle and Profond were built in the same shipyard in the same year, and thus the correspondence of the after sequences of both vessels' floor diagonals may not be a coincidence. NEXT