The distance d to the horizon from a point h feet above the surface of the earth can be calculated if you know Pythagoras' Theorem and the Radius of the Earth. Eratosthenes lived about 200 BC and Pythagoras about 500 BC. So the distance could be calculated any time after 200 BC.

It's an important number to know. Mariners especially find it useful, as do explores.

But when was it first calculated? Or rather, when was the formula first reported? I recently learned that Galisteo used it in the early 1600's when he found the height of a mountain on the moon knowing the moon's radius and the distance of the mountain from the 'horizon'.

Does anyone know of an earlier reference?

Monty, I am a complete dunce where the history of mathematics is concerned. I have checked a few source I have available but could not find the problem mentioned. Sorry.

Alex

I own a radio station in Victoria, Texas--KTXN-FM 98.7/////

The answer to your question is:
distance (miles) = square root of height transmitter in feet times 1.23 how far one can cee..

distance (miles) = square root of height of transmitter in feet and square root of square root of receiver times 1.23

To find radio horizon substitute 1.41 in each of above equations.

Joe Tibiletti, 2618 FM 1685, Victoria, Texas, 77905...
joetib@suddenlink.net, or joetibiletti@yahoo.com

in further on distance to horizon...

Consult various editions of Engineering Handbook as published by the Natiuonal Association of Broadcasters..

It has proven verey realistic for remote broadcasting for our station...In fact we broadcast a number oif football games from Port Lavaca some 28 miles from out studio
with
transmitting antenna 75 feet above ground -- 30 feet above sea level ground level
receiving antenna 75 feet above ground -- 100 feet above sea level ground level

distance (miles) 1.41 times square root 75 feet of transmitting antenna plus 175 feet of receiving antenna
1.41 x (8.66 + 13.22)
1.41 x 21.88 = 30.86 miles

Hope this helps you Joe Tibiletti

I know the formula. My question was about history. When did the formula or calculation first appear in print, or when was some reference to it first given? As I said, the first I've found was Galileo's calculation of the height of a mountain on the moon.

>in further on distance to horizon...
>
>Consult various editions of Engineering Handbook as
>published by the Natiuonal Association of Broadcasters..
>
>It has proven verey realistic for remote broadcasting for
>our station...In fact we broadcast a number oif football
>games from Port Lavaca some 28 miles from out studio
>with
>transmitting antenna 75 feet above ground -- 30 feet above
>sea level ground level
>receiving antenna 75 feet above ground -- 100 feet above sea
>level ground level
>
>distance (miles) 1.41 times square root 75 feet of
>transmitting antenna plus 175 feet of receiving antenna
>1.41 x (8.66 13.22)
>1.41 x 21.88 = 30.86 miles
>
>Hope this helps you Joe Tibiletti