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The thread: Determined up to something — page 8

Every recovery on this site returns an answer with a qualifier attached. One picture gives ratios and no size. Two give shape and no size. Many give a scene and a camera track up to seven numbers no quantity of pictures supplies. The qualifier is not a shortcoming to apologise for; it is the exact statement of what the pictures contain, and here it is counted, walked along and shown to be free rather than merely small. Essays 169 to 171 of 171.
0.050.10.20.5125105101520braccia in the pavement, drawn to one page widthpixelsthe diagonal, by straightedgethe transversals, by fittingboth read on one pavement47× at eight braccia Drawn confidently

The rule is exact for a floor that lengthens

The constant-ratio rule for spacing receding boards is an exact perspective — to the last digit, on the panel's own horizon — of a floor whose boards grow by the inverse of the ratio, 0.74 braccia deep at the front and 1.31 at the back on an eight-braccio pavement. The orthogonals agree with that floor. What says the tiles were meant to be square is a diagonal, which bends 8.1 pixels off straight where the reader's fitting test finds a sixth of one.

 the constant-ratio rulecorners off the chord by 8.03 pxAlberti's sectioncorners off the chord by 2.47 px Drawn confidently

A straightedge convicts the rule on five braccia

The constant-ratio rule for spacing a pavement's boards leaves one mark a correct construction does not: its tile corners bow off the diagonal. The worry was that a painter's hand would bury the bow in its own scatter. At a pixel of scatter it does not, on any pavement of five braccia or more. What limits the test is not the hand but the page: a pavement drawn to one width bows no more at twenty braccia than at eight, while the hand's wander keeps growing with every tile.

 -7.50-5-2.5002.50012345678tile corner along the diagonal, from the near endsigned distance off the chord (px)the rule's arc, unpaintedthe rule painted: amplitude 0.84a construction painted: -0.178 braccia, 1 px of scatterone shape, one amplitude Drawn confidently

The rule's bow is read by its shape

A straightedge on a painted pavement's diagonal convicts the constant-ratio rule by the size of its corners' worst departure, and gives out once the painter's hand scatters by a third of the bow. The bow has more than a size. It is one smooth arc, to one side, fixed by the ratio, and a hand's scatter is neither. Fit that arc with one free amplitude and the rule is ranked above a construction 96 times in a hundred on five braccia at two pixels, where the straightedge managed 83 — and the reading holds to half the bow's size in scatter.

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