Squaring Curved Figures and a Weight on an Incline
Quadrature of circular segments; a heavy body's weight divided on an oblique plane
The sheet works through the quadrature of curved figures: comparing circular segments and sectors, Leonardo argues that for any curved surface an equal square can be found, so that the surface is squarable in itself (texts 1-3). Along the right margin an inclined-plane sketch (text 4) introduces the statement below (text 5) that every heavy body producing friction on an oblique place divides its weight into two parts, more nearly equal the steeper the site. Further mechanical sketches of levers and small balances appear on the sheet but are not transcribed in the bundle.
On this page
Squaring the circular segment (a, b, n)
The half portion a equals the whole portion b, because the circle a is double that of b. From this Leonardo concludes that for any curved surface an equal square can be assigned, and that such a surface is squarable in itself.
Equal curved figures with doubled circles (a-c, b-d)
In a second figure a equals b and c equals d, because the figures are equal in value and the circles are each double the other. The reasoning is left unfinished ('If a is worth b …').
A weight divided on an oblique plane
Every heavy body that generates friction upon an oblique place divides its weight into two parts, which are the more equal to one another the more oblique the site is. The note follows a small inclined-plane sketch labelled 2-1.