# Villalpando's proportionatrix prima

Author:
RMF
Construction of the proportionatrix prima in a semicircle of diameter AG. Steps to find a point K of the curve from a point F of the semicircle:
1. Semicircle of diameter AG and center D (see diagram).
2. Semicircle of diameter DG.
3. A point F on the large semicircle is selected and FG is drawn cutting the small semicircle in H.
4. Circle of center G and radius GH.
5. I is the intersection of AG with this circle.
6. Circle of center I and radius IG.
7. K is the intersection of this circle and FG.
8. CK is perpendicular to AG.
The bottom bar of the canvas allows to follow these steps. Once the last step of the construction is arrived at, click on the 'Trace' button: the trajectory of the red point will trace the curve made by the point K when F moves on the semicircle. To stop the process, click on 'Stop Trace'. You can also draw the curve by selecting the point on the larger semicircle and moving it along the semicircle. To clean the canvas and get the initial configuration, click on the button with two circular arrows in the right upper corner of the canvas.