One thing that baffled me when I started learning about the Tychos was that known opponents to heliocentrism that were frequent in the 17th century have never been translated from latin. We can easily find Copernicus, Kepler, Galileo and Newton. But not Brahe, Riccoli or Longomontanus. And I would find it very interesting to read the books these men wrote so I did a quick tryout with chatGPT translating Astronomia Danica Astronomia danica : Longomontanus, Christen Sørensen, 1562-1647, author : Free Download, Borrow, and Streaming : Internet Archive and it turned out well I’d say even though I can not judge the translation since I don’t know latin. The promt I gave chatGPT was "Fix typos and translate to english: " And then I pasted a page from the book
It would be great to get some effort going to translate these books as verbatim as possible to engilsh since academia hasn’t managed to do that despite our taxpayer money and lots of time. Wonder why?
Dump from chatGPT:
I would be glad to help! Here is the translation of the text:
“I would like to contemplate and rely on the diverse nature of talents, inclinations of the mind, studies, and human interactions in life, O most powerful Lord. Although they are infinite and varied, they are arranged in such a way, and set in such opposition, that they can be divided into two categories without inconvenience. Moreover, just as in comedies and tragedies, the same qualities required for their representation are demanded of two captives, who were imprisoned and chained in a great king’s prison because of their own fault, and were so completely detained by the power of the king that they had no hope of escape before death. However, after both of them were granted the same exceptional mercy, which was, among other things, to be shown various and remarkable things constructed and arranged in every part of the kingdom by the same king, if they wished, they could look at them and thus alleviate the misery of their lives. One of the prisoners prepared himself with the utmost determination to obey and follow the benevolent will of this Lord, while the other, with a mindset that was more wicked, foolish, and obstinate, settled into the prison cell like a tortoise and would rather be consumed by decay, foulness, and squalor than constantly bring to mind his most beautiful memories with tears. Therefore, by what right could this person, who was so unhappy throughout his life, envy the happiness of another, or attribute the blame for his own unhappiness to someone other than himself? And so, when we are captives in this mortal body, since it has brought us such a sad condition as that experienced by all fallen parents, we wander around with such a question: “Should we flee, and where should we flee?” Yet never have we been delivered more mercifully, or invited more honorably and compassionately, from such a great prison of guilt, and to even more astonishing things.”
We believe that we can contemplate the riches and works of the universe, which beautifully fill this world of all beings, not only with our eyes, but also with our senses, until they are enclosed in the outermost boundary of the sky. Therefore, since we enjoy such great mercy from the Almighty God, who not only created this most beautiful theater of the world for our use from the beginning, but also constantly sought it out even after the deplorable fall and captivity, which we rightly deserved, let us daily persist in the omnipotent word, so that even in this exile and mortal state, while we are strangers from our true homeland, we may be able to refresh our troubled minds and admire the riches of our Creator in heaven and on earth and thus rightfully extol His praises. But above all, let us realize that the same merciful Father has had pity on our condition and captivity, so that He wanted to send His only Son to the lowest parts of the earth, and even into our mortal prison, so that our Savior and Redeemer, having assumed our flesh and sharing in the communion of the Holy Spirit, would sanctify the captivity of all believers, bring them to heaven with Him, and finally grant them unprecedented freedom, having obtained it by His precious death, conquering sin and death. We think that those who withdraw into their own prison and flee from the light are degenerate and utterly foolish, so that no happiness of the most excellent things to be known may touch them, nor may the stimulus to exercise virtue excite them, but rather the shadows, the pleasures of the belly, leisure, languor, and sloth, will infect their divine soul. Therefore, it should certainly be considered as belonging to a noble and truly heroic mind to engage in this most splendid theater of the world in such a way that it decently expresses and represents the particular condition that God, the creator and dispenser of all things, has imposed on each individual. And in the same performance, one should not neglect to exercise one’s power through the prison of this body, or the two openings of the body, as Plato calls them. For this practice is the beginning of virtues and philosophy, to first contemplate with the help of our eyes the divine works, the miraculous works, I say, in heaven and on earth; then to admire them; thirdly, to use the keenness of our mind and soul; and finally, to turn them to the praise of the Creator, not just for our use, as far as possible. From the beginning, but especially from the middle, which leads to the end, we should follow the arts and disciplines, especially, unless we are greatly mistaken, mathematics. For they affirm that nature itself is determined by an indissoluble connection of measure, number, and weight, after the sacred scriptures say that God has arranged everything. Plato testifies to this in the Epinomis with these words: “There is one universe, the figure of which is determined by numbers, harmonies, and motions of the heavenly bodies, if anyone knows any other.”
Another path to understanding, as they say, is to play with fortune. However, not anyone can be successful in these arts, which are easy in appearance but difficult to pursue. It is not to be neglected, therefore, that those who acquire the most gratifying reputation in these disciplines are of great importance. These are the words of that person. These disciplines, namely Geometry, Arithmetic, Music, and Astronomy, were demonstrated in order by Plato, from which the same number of arts emerges. When we correctly learn the last of these arts, the preceding three, which were mainly invented by the same person, are so revealed that the first two, namely Arithmetic and Geometry, are called “dry” and “plain” respectively, with which we measure the sky and the perpetual motion of the stars. On the other hand, Music is made proportional, by which we finally grasp the harmony of the superior and inferior things, and it is not surprising that these arts have always been in great honor and favor among great emperors, kings, and princes in the Republic, who, as far as possible, by favoring them, applied them to the innate magnanimity and lofty spirit of their souls. Nor is it in vain that they perceived that not the least part of successful governance, after the greatest virtue, namely, religion and true piety toward God, is fixed in these arts. For they thought nothing more absurd than to rule the world and not to know what the world is. Among the number of these heroes, who cultivated the mathematical disciplines, especially astronomy, because of its antiquity and admirable contemplation of the celestial movements, the most illustrious with noble and royal genius can be mentioned not only Magi of Pearls and Philosophers of Egyptians, from whom kings and then priests came, but also princes who were descendants of a royal line afterward. What about the first luminary emperor Julius Caesar? Was he not, in the midst of weapons and civil strife, measuring the sky with a ray? Or especially for this reason, that he might restore to integrity the most corrupt annals of that century to the true annual cycles, he rightly said these words?
“My year will not be surpassed by Eudoxus.”
What about Ptolemy of Alexandria? He was so diligent in cultivating this art in astronomy that he, aided by his own observations, completely propagated this most beautiful art, founded and preserved with his own footsteps and monuments, before his predecessors. Among Christian princes, the first was that magnanimous King Alphonso of Aragon and Sicily, who is said to have been so devoted to this art that he spent four tons of gold on the tables, which are still named after him today. What about the emperors Maximilian and Charles V? The former not only honored the celebrated astronomer Vogelin, but also himself was actively engaged in this art, and the latter was so devoted to it that he not only honored the famous astronomer P. Apian, but also himself worked in this art in the present time.
One who pursues the sublime path of mathematics and astronomy plays with fortune (as they say) and tests his luck. No one can be happy in these pursuits without facing great difficulty, yet it is also not to be neglected, as the most gratifying fame can be obtained from these arts. These were the words of a man who was demonstrated by Plato and whose work includes the names of several disciplines in order. These include geometry, arithmetic, music, and astronomy. Of these, the first three are particularly useful for properly understanding the last, so much so that the first two, arithmetic and geometry, are often called scales by which we measure the movement of the stars and the heavens. Music is proportionate, and we can only discover the harmony of the higher and lower things through it. It is not surprising that these arts have always been held in high esteem by great emperors, kings, and princes, as well as by men of the Republic who have devoted their lives to these arts when they had the leisure time to do so.
It is not surprising that they saw these arts as rooted in true religion and piety towards the one true God, as they believed it to be absurd to rule the world without knowing what the world was. Among the heroes who have cultivated the mathematical sciences, particularly astronomy, were not only the Magi of Persia and the philosophers of Egypt, from whom later kings and priests came, but also princes who were descended from royal families.
One need only look to the examples at home rather than those from foreign lands, such as the illustrious and powerful kings of Denmark and Norway, who also held these arts in high esteem. The paternal grandfather of His Majesty King Christian III, who was both serene and Christian, devoted himself to this sublime pursuit, leaving behind works of great artistry that still speak to us today.
What of the father and predecessor of His Royal Majesty King Frederick II, who was the most noble by birth and naturally gifted in the restoration of astronomy? Was it not through this extraordinary man, the greatest astronomer of all time and like another Atlas, that Urania was brought down from the heavens and placed among us in glory, adorned with the greatest royal efforts? After his great work was done, it was continued by His Royal Majesty until the twenty-first year, which, with its triple number of sevens, was fateful for humanity. This was not in vain, for nowhere in the whole world were observations of the stars more precise or significant than in Hven, where these studies were carried out.
After my innate inclination towards these studies was joined by the opportunity and the length of time, I no longer needed a teacher for anything other than nocturnal and diurnal practice. I was fortunate enough to be present at Tycho Brahe’s, not only working with his assiduous efforts but also, to a great extent, supervising his work, as all those who know me know. It was there that I deduced the incredible labor of the canon of fixed stars from the sky, the course of the moon begun and completed elsewhere, and the restoration of the remaining planets also attempted at his behest. And so it happened that a summary of the observations made by these astronomers remained with me for use, not at that time for the purpose of producing fruit from my labor but to judge the work of others around the restoration of astronomy when it is eventually accomplished. Meanwhile, I was relieved of the labors of these Uranic studies and applied my mind to other studies and activities that I thought were more beneficial to life. However, it was not to be, for the one who turned the wheel of fortune made me return to my former studies once again.
Moreover, with the help of the same magnificent Chancellor as my patron, who kindly refreshed me with the gracious benefits of the king, I did not need to think of any greater means by which astronomy could be cultivated so that the traces of Urania might be preserved for the eternal glory of my fatherland. In fact, before I crossed into Denmark, the science was almost forgotten and so obscure that the stars themselves were hardly recognizable. But with my knowledge, which surpassed that of a private individual, I was able to promote astronomy with the help of a noble patron and supporter of astronomy in my homeland, who had led me to this field of study and had brought me back to it, and who was now resurrected by God, namely the illustrious man, the most worthy successor of the Royal Chancellor, Lord Christian Friis of the Magnificent Chancellery, a knight and prime senator of the kingdom, who, with his encouragement and unique favor, kindly followed my profession, which he had recently come to admire and expertly pass on. Therefore, I quickly wrote these pages, which contain the Danish Astronomy, born and developed in Denmark, and sent them to Belgium, where they could be subjected to the careful judgment and skilled hands of the printer. This work, which I now humbly present to Your Royal Majesty, was also publicly completed in your esteemed academy in previous years, and I hope that this effort, kindly taken up by your royal favor, will be well received. For what can we not hope for from such a king, who possesses not only true piety, virtue, and clemency, but also authority, power, a more noble and truly heroic spirit, and a more subtle intelligence, to properly judge and direct these and other noble arts, and finally, a greater breadth of mind, care, and diligence?
Corrected and translated:
"To be ruled by faithful subjects, governed by just laws, to increase the wealth of these kingdoms, to fortify their borders, and to defend them as no other has commanded in the North - of whom the fame, like that of Alexander the Great, has transcended the Ganges long ago, and as we hope and desire, has won the friendship and confederation of prosperous nations. We cannot help but admire these praises given to His Majesty, as the Churches of Christ, the Academies, and the schools continue to adhere to the pure confession of faith, and constantly strive to transmit all human arts, bearing witness to the well-defended inhabitants of these kingdoms, exhibiting the strongest and best-fortified citadels and towns, some even newly arisen under the auspices of such a great King, in whom God and nature so favour that he may rightfully be considered a living and true exemplar of kings throughout Europe. Therefore, in this flourishing republic, with divine grace, the discipline of Mathematics, which has certainly been the companion of all prosperous empires, should flourish here as well, no less than Astronomy, the most noble and beautiful science of the stars, which is established in the knowledge of these shining celestial bodies, and their most perfect harmony, from which nearly infinite benefits emerge in a well-established republic on land and sea, whether it be used to explore the nature and distance of different places or to traverse the earth without error, to sail the seas on a long journey, to investigate the truth of histories, to narrate and understand the poets, to know the annual changes of the sky and the lengths of days and nodal points, to construct machines that simulate the motion of the stars, or to specify the times and magnitudes of the transitory luminaries. In the other planets, to exhibit their motions, stations, and retrogressions based on certain hypotheses. And finally, to reveal the causes of all these things to those who wish to know them. Beyond the infinite other things that flow from this celestial knowledge, it is combined with the utmost delight and pleasure, so much so that no other art can be superior, more worthy or more profitable. Indeed, what else do the poets mean when they portray Pegasus with wings, on which it would fly into the air and ultimately reach the summit of Helicon, and with its hooves, it opened the fountain of the Muses, from which Philolosophy of Astronomy began? Even the divine Plato explains this in plain words in his Timaeus. Moreover, Atlas (according to Cicero in his fifth book) did not bear the sky, nor did Prometheus chained to a rock, nor did Cepheus, when he was portrayed with his wife, son-in-law, and daughter as constellations, without divine knowledge of the celestial bodies, which the myth distorted into false names. Therefore, this art, the most ancient, most beautiful, most pleasant, and most useful of all, was born among the earliest humans (as attested by ancient Jewish history), continued among the Chaldeans, Egyptians, Greeks, Italians, Spaniards, Gauls, Germans, Britons, and Poles, and pursued with no greater care or subtlety elsewhere than here in our Denmark (which I can truly say). Since I believe that it is not insignificant for the honour of the King and the Kingdom, I endeavoured to communicate this art to all liberal minds throughout the world, so that the revolutions and configurations of the stars, as far as possible, could be extracted from it at any time, and in applications far greater than the present, they could be handed down to posterity as an eternal legacy of the sky. Indeed, I am trying to serve this purpose with my limited
translate: Laus fpeciosa poetrse concinit, ipfa veritas
Perpetuum vires tempus & aevum manent.
Tu quoque prajclaras terrae vertentis in orbes,
Quas docuit Musis indagare, renovas.
Vim tibi divinam tribuit caelestis honorem,
Arte suam quam cuncta creavit Deus.
Omnibus hoc facinus meritis magnum & impar,
Et tibi quod nullum Par tribuit genus.
Tu vivas, floreasque diu, quam maxime, Princeps,
Et famam artificiis vincere debita tuis.
Haec ergo coram Christo laudes effundo,
Suppliciterque precor Deus his adsis opem.
The beautiful praise of poetry sings, the truth itself
Endures forever, with perpetual power and age.
You also renew the splendid circles of the earth,
Which you taught to explore with the Muses.
Heavenly power has given you honor for your divine talent,
Which God created for all things with his art.
This great and unequalled achievement is deserving of all praise,
And to you, no other equal has been born.
May you live and prosper for a long time, most noble Prince,
And overcome the fame owed to your talents.
Therefore, in the presence of Christ, I pour out these praises,
And humbly pray to God for his help.
I may emit into the light of day a useful work for all mathematicians by re-examining from the beginning the solution of triangles, a topic to which I had dedicated myself earlier. It was an endeavor that required more intricate geometry, which governs its practical application, and thus was preserved, so that it could emerge in a true and authentic way through the use of the cannon and this instrument’s correction and refinement by an actual discovery of trigonometry. Nonetheless, once I found an artist suited to this work in the Netherlands, namely Willem Janszoon Blaeu, a highly skilled mathematician and my former colleague, who has employed all possible diligence to give lustre to the products of his workshop and who I thought might assist in this enterprise, I decided to condense the trigonometry of plane and spherical triangles into the most brief and easy-to-use compendium, and thus make it more common and esteemed by those who teach it in universities, and to allow it to be more highly recommended to scholars by the fact that the foundation of astronomy, which practically encompasses all of mathematics, depends almost entirely upon the solution of triangles, which is the first and foremost topic in this discipline and in which all other topics are resolved through analysis. Indeed, Tycho Brahe himself once said this of trigonometry. Everything which the learned mathematicians have invented in this field reveals its secrets, as it opens whatever Olympus has kept locked up. R Vieta, too, when he suggested the hypothesis of the cannon for mathematicians, posited that the glory of mathematicians lies in being able to equate angles and sides, and to solve all sorts of triangles, both plane and spherical, with happy and amazing calculations. The same practice should also be followed as that of the ancients, Ptolemy and Copernicus, lest I seem to want to fly into the heavens and display a path unknown without the use of arithmetic or geometry. This is also why, in my judgment, I have chosen to first delve into the nature and arrangement of the sky and the great bodies of the universe, as it is in keeping with the pages of scripture and is fitting for reason and nature. If, indeed, these things are not moderately known, the queen of all disciplines, astronomy, cannot be properly taught, understood, or resolved, nor can it be adapted to practical use. Nonetheless, I thought it best to first mention this well-meaning effort, and to do so repeatedly when necessary, for other areas where it is more frequently required. As for astronomy, it is no less superfluous to commend it anew to those who already understand it, and it would be like trying to sell wine on which ivy had grown. In the meantime, if someone benefits from my watchfulness and labor in this work, I will consider myself fortunate since I have accomplished nothing else in life than to be able to put this effort to use for the benefit and gratification of others.
The doctrine of the analysis of triangles is an extremely ingenious method of producing any fourth or all other triangles by means of three proposed triangles, according to the same analogy in producing their corresponding sides. The doctrine of the analysis of triangles, as it is presented here in a condensed form, consists of two parts. First, general statements are made about the definition and division of triangles, along with certain geometric theorems, the assistance of which is crucial for the analysis of any given triangle. Here, it is also shown how the three-part canon, which consists of tangents and secants, and which is designed for solving triangles, depends on this structure and continuity through numbers.
Then follow the accompanying solutions of triangle analysis, which are twofold. Either the analysis is directed generally to any given problem, and falls under the rule of the golden proportion, where either the usual practice in arithmetic is followed, or the more concise method of investigating the quantity of the hidden term, such as the fourth, etc., by means of proportionate ratios. Or, the solution is adapted to the species of proposed triangles, both plane and spherical, with reasoning that is properly adapted to each particular theorem that precedes it.
And so, this order, this summary of our doctrine of the analysis of triangles, will be in the vestibule of our astronomical work. If one asks further why many theorems are put forward for justification by means of convenient inductions in the course of analytic subservience, the answer is also forthcoming. These are presented only to avoid being overwhelmed by the multitude and bulk of such things, which, when cultivated and demonstrated in their entirety, are derived from their sources to this end through numerous channels.
ABOUT THE FIRST PART
A triangle is a figure consisting of three angles and as many sides. Therefore, in every triangle, three angles and three sides are considered. In order to facilitate subsequent computations, degrees of circles are usually divided into 360 parts, or degrees, with each degree consisting of 60 minutes, each minute consisting of 60 seconds, and so on, ad infinitum, depending on the required precision. Hence, the sexagesimal arithmetic, which is also called logarithmic, has its origin. In some places, degrees are marked with an o, minutes with a ', seconds with a ", and so on, when logarithmic numbers are used.
There are some typos and errors in the text, but here is the corrected and translated version:
"More justly should we admire, or blame ourselves, if before following the footsteps and movements of the greater celestial and terrestrial bodies, namely the stars and the earth, we do not first investigate suitable hypotheses concerning the nature and definition of the space and bodies of these substances, as well as their movements in the universe, and also concerning the nature and form, especially of the said celestial bodies, as it will be more convenient to see the conservation and movements of these bodies as continuously influenced by divine influx. Finally, we will present a few astronomical observations concerning the consideration of time and motion.
Indeed, without this moderate knowledge, an astronomer will neither be able to sufficiently trace the proper places and movements of these bodies, nor to scrutinize their influences and operations even in these sublunar conditions. And although we acknowledge that this inquiry properly pertains to Physics, we do not believe it will be foreign to the profession of an astronomer, but rather appropriate for it. For someone who contemplates the supra-lunar or celestial nature is an astronomer, and for this reason (all other things being equal), no one can be more elevated in their sense and reasoning towards it.
As for the first part of our proposal, we first reject the opinion of those who believe that the celestial region is hard and impervious. Indeed, it is filled with such material orbs, as the Peripatetics, whose error without doubt descended from the dogma of Pythagoras about the musical harmony of the celestial orbs, did not understand. Secondly, we reject the opinion of those who believed the ethereal region to be fire, like certain Stoics whom Theophrastus imitated. Unless it is understood to refer to the stars themselves, or to the primary light everywhere through the sphere, and the traces left in the stars are obvious, it is rather to be conceded to God than to anything created, and sometimes it is necessary to presume that it has disappeared, as in the Appendix of Astronomica about new celestial phenomena. Finally, we reject the opinion of those who believed the same celestial region to be either the air of the fixed stars, or the water of the constellations. For when, especially in our times, there are more accurate determinations of the positions and movements of recent phenomena, especially celestial refractions, and other indications that are encountered by an experienced astronomer, most of their reasons are convincingly refuted. Without a more extensive argument, we believe, according to Sacred Scripture, nature, reason, and finally experience (as it appears to us) that the matter of the visible and finite universe, suitable to its nature and fullness, is an extremely subtle and rarefied substance, which we call the most subtle and impalpable expansion, and its essence is stable."
The merit of marveling should be either attributed to us for turning our attention to the subject, or to our fault if we neglect it. Thus, before we follow in the footsteps and movements of the larger celestial bodies, namely the stars and the earth, we must propose suitable hypotheses regarding the nature and definition of the place, substance, and movement of these bodies as well as their general nature and form, especially the conservation and continuous movement of these bodies through divine influence. Finally, we will briefly discuss the few phenomena of astronomy in relation to time and motion. An astronomer without a moderate knowledge of these things will not be able to properly study the positions and movements of celestial bodies or investigate their influences and operations even in sublunary matters of nature. Although we admit that this investigation properly belongs to physics, we do not believe that it is irrelevant to the profession of astronomy, but rather that it is closely related to it. In fact, anyone who contemplates the supra-lunar or celestial nature is an astronomer, and (all things being equal) no one can be more elevated in their sense and reason than in this contemplation.
As for the first part of our proposition, we reject the opinion of those who believe that the celestial region is hard and impenetrable, such as the Peripatetics, whose error undoubtedly arose from the Pythagorean dogma of the harmony of the celestial spheres. Secondly, we reject the opinion of those who believed that the celestial region was composed of fire, such as some Stoics, whom Theophrastus and Paracelsus imitated. Unless this refers to the stars themselves and the primordial light spread throughout the universe, and leaves visible traces in the stars, it should be believed to have vanished, like in the Astronomer’s Appendix on new celestial phenomena. Finally, we reject the opinion of those who believed that the celestial region was composed of either the ether of the stars or of water. As we have learned in our time from more precise observations of the positions and movements of recent celestial phenomena, especially the refraction of stars, among other indications that are encountered by experienced astronomers, most of these reasons are proven wrong. Without lengthy refutation, we will briefly present our opinion on this proposed topic, which we believe is most suitable for Scripture, nature, reason, and finally, experience.
The matter suitable for the visible and finite universe, according to its nature and fullness, is a substance that is expanded, thin and subtle, and is called the rarefied and incorporeal medium. It is also subject to a certain quality of cold, like that of light and the glow of stars, especially the primary cause of the separation of waters. The first reason for this definition is that no natural light, insofar as it emanates from its luminous body in space, can be transmitted through a vacuum or without a medium. Light or radiance is only an accident that occurs outside its root. On the other hand, fire and all bright bodies emit light and radiance because of the effect of the stars, especially the Sun, whose rays not only reach us, but also penetrate the very earth in the formation of metals.
Therefore, since such light cannot be transmitted simply through a vacuum, it follows that it requires some kind of medium that has a defined nature, as we will confirm later. The first proof is that such a homogeneous and similar material exists. If it were otherwise divided, another would exist in the ether above the moon, and another in the sublunary region, differing from the former, where the light and radiance of the stars would spread to us. Therefore, only air can exist here. But we do not recognize that such air is an immediate vehicle of light or radiation, even in