Geometry: the line through two equal circles' intersections
Proof that this line is equidistant from both centres, with intersecting and tangent circles.
Leonardo states and proves the 1st proposition: if two equal circles intersect, the straight line through their two intersection points is everywhere equally distant from both centres. The proof rests on the definition of the circle, since the equal circles have equal radii, so a-e equals b-e and a-n equals b-n. A diagram at upper right shows the pair of equal intersecting circles with their common line; the caption also names a pair of tangent circles.
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The line joining two equal circles' intersections is equidistant from both centres
Let the intersecting circles be a-t-n and b-t-n, with intersections t and n. Leonardo argues that the line d-e through these intersections is equidistant from each centre because a-e equals b-e (equal radii of equal circles), and likewise a-n equals b-n, so every part of the straight line t-e is equally distant from both centres.