As part of my Religion and Science sabbatical theme regular readers of this blog won’t have missed my interest in mediaeval bishop-scientist Robert Grosseteste, and in particular – because it’s an area I have some background in – in a fifteenth century treatise on the liberal arts that draw heavily on his writings. The treatise was extended at some point to give extra very practical material on measuring things – rather *Scouting for Boys* in style, but very necessary given the technological conditions of its age.

A key tool for measuring heights and depths was the **quadrant**, a quarter section of the more familiar **astrolabe** as described by Chaucer (the same scribe wrote the manuscript of “my” treatise as wrote some of the Chaucer ones) – and curiously a pocket-size quadrant was found just ten years ago in an excavation at Canterbury, dating from 1338 (you can tell from the astronomical marking used what date is meant for), and saved for the nation by the British Museum where it is now one of their highlights (http://www.britishmuseum.org/explore/highlights/highlight_objects/pe/a/canterbury_astrolabe_quadrant.aspx). Chaucer was born in 1343 so it all fits together rather well!

For fun I’ve printed out the image of the quadrant on card, stretched back to its proper shape, cut it out and made my own. You can see how tiny it is by the old threepenny-bit that got pressed into service as its plumb-weight. And it has to be said that markings are by no means those of a precision instrument; but nevertheless I’ll be having a go at using it. Hope I’m not late for any appointments…

Here’s how my medieval treatise says it can be used to measure the height of a tower:

If ye wil knowe the height of a thyng bi his quadraunt or triangle, behold and considre the hiest part of the thyng thurgh both holis of the quadraunt, and go toward or froward the thyng til the perpendicule plom fal vpon the mydlyne of the quadraunt, that is to say vpon xlv degrees. After this ye shal take the length fro youre eye to the erth and marke the place of your standyng and mesure to the grounde of the thynge that ye mesure, and put therto þe length from your eye to your foote, and al that to guyder shal be the mesure of the altitude that ye wil have, as is shewed in picture.

The essential “picture” or diagram got lost in transmission so here’s one I prepared earlier:

Using the quadrant to sight the top of the object at 45° sets up a pair of similar isosceles right angled triangles, the first of which ABC has sides equal to the height to be measured and second of which FGC has equal sides being the distance from the eye to the ground and the distance from that ground point to the point where the hypoteneuse strikes the ground. Adding the distance between the point beneath the eye and the base of the object (BG) and the distance between the eye and the point beneath it on the ground (FG which equals GC) gives the length BC which is equal to the length AB, QED. And phew!