(no subject)

[stellar_muddle]

So after a day spent looking at Da Vinci Machines, rushing around the local museum and avoiding the heat (a high round 41 degrees C... and down to 33 degrees now), this seems somewhat appropriate. Anyone know how to use it? We played a little with sextants in first year astro labs, but they had put a few extra bits on by then. I am fairly certain it wasn't used as a pocket calculator though and I wouldn't class it as ancient...

And for those who are fans, Andy Irvine is currently in NZ touring. Good music and from the half a concert Z and I caught several years back in Chch round Valentine's Day, a good live show. Missed him in Aussie this round, but he only hit Melbourne and Sydney region anyway, so wouldn't have helped to know.

Comments

[vonstrassburg.livejournal.com]

Pity the photos are too small to tell what the markings are, but: The front (not the side with the eagle) has a logarithmic protractor on it, you can use it to measure angles, or perform multiplication and division calculations like a slide rule, or a combination of the two (useful for measuring heights and distances if you have a reference point). The stylus, which pivots around the nut at the right angle corner of the quadrant, is missing. The back contains a simple rotating calendar -- although you need to rotate it mentally because it doesn't slide by itself like a modern one. There is also a simple table of solar noon corrections on it which can be used, in addition to the stylus and the protractor, to measure the sun height and calculate the time of day (like a sextant), although you'd need a separate set of sight reduction tables and an almanac for that, and you'd need to know your exact location. Unlike a sextant it doesn't work in reverse, so you can't figure out your location from the device and the known time (except a latitude sight at solar noon). In any case a proper sextant with mirrors and stuff would be more accurate for taking sights.

The angle of the eagle's wings would be set so that one of the wings formed an angle with the ground equal to the latitude of the known point at which the instrument is designed to be used. e.g. at London, approx 55 deg north, the device would be built so that one of the straight edges formed an angle of 55 degrees with one of the eagle's wings. So the quadrant is built to be used at a particular place (e.g. London), and a different one would be needed in, say, Paris or Rome or Adelaide.

[stellar-muddle.livejournal.com]

Logarithmic protractor would be useful for calculations. Any idea when they started using them? A brief look at the history of Logarithms on wikipdia attibutes public description of the method to a paper by John Napier (Baron of Murchiston) in Mirifici Logarithmorum Canonis Descriptio in 1614, which is well after 1388. Trade secrets amongst shipping guilds or builders? Missdated? Or just Wikipedia being confused...

[vonstrassburg.livejournal.com]

It's not a true logarithm, because it isn't built on a linear logarithmic scale and can't produce arbitrary products. It is based on a "golden rectangle" algorithm which can be used to produce products and factors of sines and cosines of particular angles, which is all that is needed in this case. It is, however, essentially logarithmic in scale for those sines and cosines -- hence "logarithmic protractor" not "slide rule". Check the curve on the photo if you want to do the maths yourself.

Golden rectangle algorithms have been in use since Pythagoras.