Chords, arcs, and the equal angles of reflection

Equal chords and the midpoint of the curve

When the two lines a e and c h are of equal length, the middle of the line a c strikes upon the middle of the curve i h, that is at f. If instead the lines b a and b c are unequal, the relation changes.

The eye, the image, and equal angles of incidence

Let n be the real object and e its image; m is the eye. The image also lies at the centre of the circle b e S, which cuts the equal angles that place the angle of incidence at point c. The angles of incidence are equal to one another, as shown by the two triangles a c b and d e c.

Tangent of a chord parallel to another line

When the straight line c b is parallel to the straight line a b, the contact that c b makes with the arc a n o falls at the middle of that arc. If the line a b descends, the point of contact shifts accordingly.

A short calculation with 1000 and 12

A brief arithmetical operation sets the number 1000, written twice, against 12, worked out in the margin among the geometric figures.

Metà destra. Figura con:

Figura con:

Figura, con:

Metà sinistra. Figura:

Figura:

Figura:

Figura, con:

Figura, con:

Operazione aritmetica:

Right half. Figure with:

Figure with:

Figure, with:

Left half. Figure:

Figure:

Figure:

Figure, with:

Figure, with:

Arithmetic operation:

Chords, arcs, and the equal angles of reflection

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Equal chords and the midpoint of the curve

The eye, the image, and equal angles of incidence

Tangent of a chord parallel to another line

A short calculation with 1000 and 12