Proportion of circle-portions; tracery and vault designs
Similar segments keep the ratio of their whole circles; drawn rose-tracery and vaults.
The note argues that similar parts of circles hold the same proportion as their whole circles, illustrated by dividing a circular segment into whole, half, quarter and eighth portions (ace, abcf, abf, anf) and on to infinity into equal sectors. It also states the Euclidean theorem that all triangles built on an equal base between parallel lines are equal. The lower half of the badly stained sheet is filled with drawn semicircular tracery fans, star-rosettes and ribbed vault or dome studies; further untranscribed notes appear at the upper right.
On this page
Similar circle-portions keep the ratio of their circles
The proportion of the similar parts of circles equals the proportion of their wholes: from circles in double proportion, quarter-circumference portions give chords in quadruple proportion; and where two portions differ in sixteenfold proportion, the sixteenth part of the greater equals the whole of the lesser. It is a study of how segment size scales with circle size.
Dividing a segment into portions to infinity
In the labelled figure ace is the whole portion, abcf the half, abf the quarter and anf the eighth, and so on to infinity, the portions being divisible without end into equal sectors of equal length. Alongside, all triangles made between parallel lines on an equal base are declared equal.
Tracery fans and ribbed vault studies
The lower part of the sheet carries drawn semicircular designs: sunburst fans, star- and petal-rosettes set in circles, and half-domed or ribbed-vault sketches. They read as geometrical ornament for windows or vaulting rather than as text.