old nomenclature no longer used

[galactus]

Looking through some old surveying books, I have ran across the terms:

exsec(x) and vers(x)

exsec(x)=sec(x)-1 and vers(x)=1-cos(x)

The latter is known as 'versed sine'.

The exsec, I am not sure. Perhaps 'external secant' or something.

Has anyone seen these before or used them in the past?.

They are not taught anymore as I am aware of. I have never saw them in a class of any kind, only in these old surveying books.

 

[daon]

Re: olad nomenclature no longer used

I've never seen them. What are the applications of these functions in the surveying books?

vers(x) is mentioned in this calculus book.

And both, along with haversine, excosecant and chord are mentioned here: http://wapedia.mobi/en/Trigonometric_functions?t=9.

 

[galactus]

They were used back when surveyors had to do calculations by hand. Before the days of calculators and data collectors.

In those days the trig tables or a slide rule were used. Also, logs were used a lot to simplify calculations.

I picked up some old surveying books a while back at a used book store for a song. The math is still the same. I self-taught trig from these books way back in the days before college.

I have 'Surveying Practice' , 3rd ed. by Kissam. It has a chapter called Trigonometry in Surveying. Logs are used extensively along with the trig.

This book is from 1978, so they do mention doing them 'by machine'.

Ex: Given a triangle with angle \(\displaystyle A=38^{\circ}54'37'', \;\ a=326.39, \;\ b=508.69\)

One solution:

\(\displaystyle log(sin(A))=9.798031-10\)
\(\displaystyle \;\ \;\ -log(a)=2.513737\)
-------------------------------------------
\(\displaystyle log(sin(A/a))=7.284294-10\)
\(\displaystyle +log(b)=2.706453\)
------------------------------------------------
\(\displaystyle log(sin(B))=9.990747-10\)

\(\displaystyle B=78^{\circ}12'53'', \;\ or \;\ 180^{\circ}-78^{\circ}12'53''=101^{\circ}47'07''\)

And it goes on. It also uses some pretty cool stuff to find area of a land tract.

The book that mentions the exsec and what not is from 1951. It is called Route Surveys by Rubey.

It has the identities in the back, such as \(\displaystyle exsec(2A)=\frac{2tan^{2}(A)}{1-tan^{2}(A)}\)

It also used calculus to derive the formula for a spiral curve and all that. I have learned some neat things from these books.