The journey began around Easter 1727 and continued through Silesia, stopping several times until they arrived at the regiment's headquarters in Litschau on 28 June. The following month, they moved to quarters in the Upper Hungarian capital of Kaschau [now Košice]. ... Both in Silesia and in Hungary, he observed everything that could increase and enhance his learning, experience, and purpose. He was concerned with discovering the riches of nature, not only above but also below the earth, in the famous Hungarian mines.

A journey he made in 1728 via Ofen [now Buda and part of Budapest] to Vienna provided him with a wealth of architectural masterpieces in this magnificent residential city, which he was only seeking in accordance with his ultimate goal. On his return journey to Stolberg in 1729, which involved detours via the Hungarian mining towns of Neusohl [now Banská Bystrica], Schemnitz [now Banská Štiavnica], Kremnitz [now Kremnica], and others, he greatly increased his insight, especially when he was able to inspect the special copper mine at Schemnitz and the rich salt mines at Solivar near Eperjes [now Prešov]. He arrived in Stolberg at the beginning of August, and his illustrious Count found his services so faithful, his skill so enhanced, and especially his experience in chamber and mining matters so exceptional, that at the beginning of 1730 he appointed him chamber and mining councillor and simultaneously entrusted him with the directorship of construction.

Geometry, by definition a science that measures lengths, angles, areas, and volumes, is a subject beneficial to the common good, and is specifically recommended. True, some may regard practical geometry as a trivial matter, as if it should be a little overlooked; but such despisers will thereby make themselves more contemptible than this magnificent science among intelligent people. But I must not attempt to explain in many words how practical geometry is for the common good, since the matter speaks for itself. Just imagine, if a plan of a country estate, with all meadows, fields, forests, and other relevant details, has been accurately measured, neatly put on paper, and marked with the appropriate notes, according to the instructions of this treatise, how pleasant is this for the observer, but especially for the one who has charge of the country estate? The former can immediately get an idea of ​​the current location and condition of the estate, and the latter surveys that which he had to go through over many times, like someone who has done a lot of ploughing and can recap it in an instant on a land chart. On this one finds how many acres each piece has, according to which one can make different arrangements, both for sowing and for other purposes. One notes where all the pieces adjoin, and, if they are divided up, one can immediately judge how they can be conveniently exchanged or otherwise improved. In legal matters one finds out where boundary stones, pillars, piles or trees were, etc. Because of the hereditary rents and other dues one can immediately see what is attached to each piece of land, be it house, farm, garden, meadow, etc. or what it must do for service, and the like, if this has been recorded in detail on the plan. In this case, such a plan serves far better than a hereditary register or inventory book. ... If a lord has large forests and wants to manage them economically so that the wear and tear always remains the same, a geometric plan can be a good basis for this. ... The benefits, advantages, and convenience of accurate ground surveys on large game reserves in terms of profit, advantage, and convenience for organising substantial hunts, as one can regulate all drives in advance on paper, calculate the number of blinds, nets, and tackle, and make other clever arrangements, is not unknown to experienced hunters. The beneficial assistance that water weighing provides in mill construction, water pipes, and pipe laying is never sufficiently praised by those who are involved with it. To touch upon several useful aspects, including the entire art of weighing, would be too extensive. From what has been presented here, one can already be convinced of the usefulness of practical geometry. This has indeed been considered in both ancient and modern times.

It will not be wrong to call the mathematician a miracle worker. While they cannot perform supernatural miracles, as was believed in ancient times, which is why mathematicians had a bad reputation at that time, they are nevertheless capable of performing natural miracles, which even today strike some inexperienced people as supernatural things and are considered by them to be supernatural, but their assessment neither detracts from the matter nor glorifies or magnifies it. ... Let us briefly consider the applications of mathematics. We find that arithmetic brings very hidden things to light and makes completely unknown things known. Geometry allows us to measure things according to their sizes and distances, which one cannot otherwise attain. Civil architecture constantly multiplies the numbers of the world's real wonders. Military architecture teaches us how to protect our possessions from a great multitude of powerful people; conversely, it shows us ways to master insurmountable ramparts and walls. Naval architecture builds the most impressive castles, which have neither foundation nor permanent situations, yet can still captivate. Pyrotechnic thunderstorms shatter gates, ramparts, and walls, but also create very entertaining spectacles with rising and flying objects that have no wings. Mechanics performs astonishing miracles. Even if Archimedes' statement that he could lift the Earth from its place if he had another place where he could have a firmer footing to do so, passes as a great boast, it is nevertheless certain that the heaviest loads are lifted with little strength, and often 100 pounds are outweighed by one pound. Astronomy takes us to other worlds. Acoustics makes the deaf hear. Optics, I dare not say that it makes the blind see, but it strengthens naked eyes in such a way that they see clearly what seemed unclear to them, or which they were probably not able to see at all; it makes visible things which are completely invisible because of their smallness and distance; it causes us to be able to look ourselves in the eyes and examine all parts of our face ...

In his treatise "Bau-Anschlag" (Building Estimate), first published in 1743, Johann Friedrich Penther declared the creation of comprehensive, detailed, and precise cost estimates to be the sine qua non of all construction projects. It therefore seemed all the more incomprehensible to him that "no one would want to be seen showing the way how one could arrive at a determination of all future costs for a building to be constructed."