How to make world map from hand? (EARTH) :)

[Hai-Etlik]

It depends what you mean by "proportional". You simply can't flatten a globe into a flat map without distorting things. You can preserve areas, at the expense of shape/angle, and you can preserve shape/angle at the expense of area. In between you can also preserve distances, but only though a particular point (For instance, you can preserve distances that are along lines going towards or away from the poles, but distances along other lines will be distorted). You can also make maps that try to balance out what is distorted and where to give a reasonable if imperfect overview.

That doesn't mean you have free rein though as the particular distortion of a projection is quite specific.

A common map projection used for world maps in the 17th century is Stereographic, typically in the form of two hemispheres. This is one of the shape preserving projections ("conformal"). To draw the graticule for such a map, you need to be able to draw precise arcs of very large circles centred well off the map. Once you have the graticule, you can use it as a guide for drawing the features on the map.