Port of Civitavecchia, church plans, and laws of the balance
Harbor and dock measurements amid domed churches, weight-and-obliquity propositions, and triangle-angle theorems
A densely worked recto crowded with architectural studies of domed, centralized churches in plan and section, arcing harbor works, mechanical sketches and a small terrestrial globe. Measured plans of the port of Civitavecchia and its dock are drawn among them, and a central globe carries the note 'how the course of the wind is straight.' Three columns of text set out propositions on balances, showing how equal weights and arms can still yield unequal results when the obliquity of the motions or of the pendants differs, while a further column treats the 'real' and 'potential' angles of triangles cut by their axes. Additional matter includes a cord bent by a weight, arithmetical operations (64, 512, 4096) and short fragmentary lines; further untranscribed writing fills the sheet.
On this page
Studies of domed, centralized churches
The sheet is filled with plans and sections of centralized churches carried on domes, drawn in light ink among the notes. These architectural studies are not covered by the transcribed text and are described from the drawings.
Measured plan of the port of Civitavecchia and its dock
A harbor plan with arcing breakwaters is lettered with measurements 100, 334, 100, 220, 220, 220 and 351, and a dock ('darsena') marked 200-300. The figures record the dimensions of the port works of Civitavecchia.
Equal arms and weights that still remain unequal
When the weights, the arms and the obliquity of the motions are equal but the obliquity of the pendants is unequal, the weights show themselves unequal. Conversely, if equal weights on equal arms move one another, then their motions must be of unequal obliquity.
The real and potential angles of a triangle
A triangle cut unequally distant from its base is not divided equally by its axis. Every obtuse real angle has its potential angle outside itself, every acute real angle within, while a right real angle is at once real and potential, the potential angle always being a right angle. Labels a b c and a d b are used.