How people used to do it in past. Atleast we must know how to determine panchangam
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You don't need internet for that purpose if you have an Ephemeris with you.
For example, the book Raman's 110 years Ephemeris will allow you to compute any horoscope provided the birth has occurred between 1891-2001 A.D.
Similarly, the book Raman's New Millennium 50 Year Ephemeris (2001-2050 AD) will allow you to calculate any birth charts for the period 2001-2050.
And, apart from that, there are plenty of softwares available too (some of which are completely free to use), which also will help you in casting the horoscope even if you don't have access to internet.
Astroloka is one such free (but highly featured) software. It has already been loaded with an Ephemeris.
And with it you will be able to calculate any charts with birth being happening in the long period of 1800-3000 AD.
Horoscope can be calculated from 1800 AD to 3000 AD.