Octagon construction, a balanced scoop, and fire rockets
Geometry of an octagon, the balance of a filled scoop, launching rockets, and a single-tooth wheel.
This densely worked verso mixes a geometric method for building an octagon on a given line with two studies of a balanced scoop that weighs down less when full than empty. A column of notes describes launching a rocket from a crossbow and driving fire rockets aloft, and another observes that a wheel moving a load with a single tooth of its shaft can shift more weight than with two. Several columns of figures run down the margins. Cube-and-grid perspective sketches near the top are not covered by the transcription.
On this page
Constructing an octagon on a given line
To make octagons on a given line, take it as the base of an equilateral triangle and divide the base into 3 equal parts. Set one part on the angle opposite the base along the axis line; where that division ends is the centre of the circle that contains 8 such lines.
Balance of a scoop, full versus empty
With a, b, c as given, the excess outside the pole of the balanced scoop is one third. Fill the scoop so it weighs 20 pounds with a one-pound handle, and the excess becomes a twenty-first, so the scoop dips less when full than when empty.
Launching a rocket from a crossbow
Shot from a crossbow the rocket goes high; kindled with fire once the bow has raised it, it is carried far aloft. Made of iron with a ball ahead to guide its flight, it shows a tail of fire the whole way. Fire the rocket before the little bombard and the greater weight guides the motion.
A wheel that moves a weight with a single tooth
If a wheel moves a weight with a single tooth of its shaft, it will move a greater weight with the one tooth than with two, because of the impetus it gathers when it works without effort.
Marginal columns of figures
Long columns of numerals run down the right margin and near the central fold of the sheet. They appear to be tallies or computations accompanying the balance and mechanical studies.