braccio — where it appears
Named by 7 essays across 2 fields — each of them below, with the objects they name alongside it.
Alberti draws a pavement, and chooses where the reader stands
The costruzione legittima of 1435 is exact. Run as a construction — with drawn rays and drawn intersections rather than the formula it turns out to satisfy — it agrees with a pinhole camera to six parts in a hundred trillion of a pixel. And it has one free parameter that the recipe never names, which is the distance from the eye to the panel.
A steady creep draws the rule's bow
The arc reading was built to find the constant-ratio rule by the shape its pavements bow the diagonal. A correct pavement painted by a hand that lets each transversal gap grow 4.5 per cent on the last bows it the same way — to 0.31 pixels, a cosine of 0.9994 — on eight braccia, and 1.5 per cent is enough on twenty-two. The arc reading measures how much a pavement's tiles lengthen, not what lengthened them, and against its counterfeit it is a coin. The rule's own definition still tells them apart: its gaps' logarithms are straight, a correct pavement's bend. Read to half a pixel, that names the rule on eight braccia 94 times in a hundred.
A panel's pavements convict the creep one pavement hides
One crept pavement bows its diagonal exactly as the constant-ratio rule does. A whole interior has several — a floor, a step, a table's inlay, a loggia's coffers — and the rule bows each by the same share of its own bow, where one steady creep bows a twelve-braccio pavement 1.72 times as much and a four-braccio step 0.62 times: four pavements painted to a pixel name the rule against it every time. A creep tuned pavement by pavement to counterfeit every bow is caught instead by the gaps, whose curvature has one sign on every correct pavement: four pavements name the rule ninety times in a hundred at a pixel, eight pavements ninety-seven.
Three procedures, one panel
Alberti's lateral section, the distance-point construction and a pinhole camera put every transversal at the same pixel — and every reading of the finished drawing therefore returns the same number for all three. The methods are distinguishable on the desk and indistinguishable on the panel, which is the fact any attribution has to start from.
A panel's creeps keep the order it was painted in, while the hand is steady
A painter who tires lets each pavement's gaps creep a little more than the last one's. Fit each pavement's creep from its transversals and rank them, and the ranking is the order the panel was painted in: with the creep growing a point a braccio from one pavement to the next and the hand at a pixel, the whole order of four pavements comes back fifty-seven times in a hundred, against one in twenty-four by chance. The step is the weak link — four short gaps fix its creep to two points — and a creep set by each pavement's length rather than by time reads as a confident order that is not the painting's at all.
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.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
AttributionPavementConstant-ratioFalsifiabilityleast squaresResidualStraightedge constructioncostruzione legittimaTransversalViewing distanceCentric pointCross-ratio