The letter of Jacob Kurz of Senftenau published by Tycho Brahe in his Mechanica

Translated by Alena Hadravova and Petr Hadrava 1997, Acta historiae rerum naturalium necnon technicarum, New series Vol. 1, 79-89: Tycho Brahe and Prague (proc. of conference Science and technology in Rudolphinian time) on the base of Tychonis Brahe Dani Opera omnia I-XV, ed. I.L.E. Dreyer, Hauniae 1913-1929: V, 119-124. and the first edition of Astronomiae instauratae mechanica, Wandesburgi in arce Ranzoviana prope Hamburgum, propria authoris typographia 1598.

Many greetings
Thank you very much, the noble and very educated man, for your will not only to address me by your letter but also to offer me kindly your favour. Despite I have not seen your good face, yet a long time ago I beloved and esteemed your soul from your treatices by which you consecrated yourself to eternity. For this reason I became anxious to see you in reality, to bow to you, to embrace no less eagerly than those who once set out from the outmost parts of Hispania to the City1 to see Livius2 This my wish was amplified by your kind urge and it was amplified so much that if the will of the Emperor and the reason of my public duty would not prevent me then, as the Lord is above me, neither the distances and sufferings of the journey nor the love and grace of my most beloved wife and the sweetest pledges would prevent me to hurry to you into Denmark taking with me as a companion to the travel our common friend Thadeus Hagecius. I can not tell how I like to explore in mind the whole Hven - if we can not in reality - and especially your absolutely precise observing instruments and finally, despite only in imaginations to comprise the whole mathematical system. And even if I would be present and if I could as a spectator to see you yourself not only to explain everything but also do it in practice. However, because I can dream of it but scarcely to hope in this time (despite I did not throw away the hope entirely), I returned to your letter and I will reply in a few words on its most important parts. First of all this. That you are looking up my opinion on your treatises and you put to my judgement not a quarrel but rather friendly dispute with some very learned men, already by this you are paying me a honour, which I would not esteem so much if some discorded kings and leading men of kingdoms and whole countries would appoint me to be their judge. However, neither my education, which I have not at all or only a negligible one, nor my modesty allow me to do what you are asking and suggesting. Because I am not completely deaf to so friendly a challenge, remember the following. What I think in general about your treatises it is testified by the privilege of His Emperor Majesty, which I am sending in the enclosure of this letter.3 I am the author of this as the Emperor wrote it and I was also guarantor that the Emperor is saying truth in it. Especially that, what you have recorded and confirmed by very reliable justifications on the recent comets observed by you, is such that the scholars can not doubt any more. So I am not forced to believe that those, who stay still between the hesitants and who are making themselves look like they defend Aristotle's authority against the verified truth, really do think so. I suppose they are doing it rather to move the whole stone and to explore from all aspects everything, what could seem to confirm the idea of Aristotle and to shake or to rise doubts of yours idea. They would present it to you as a Lydian stone4 to investigate and in this way they will yield you the chance to spread out by the Sun of your education not only all darkness of mistakes but also even the lightest cloudlets and to complete the teaching on these things for the followers. If they clash with you with such an intention, I am certainly maximally partial to them; if, however, they behave otherwise, I assume their willfulness ought to be disdained. The treatises which they enforced by their willfulness from you for the common benefit demonstrate what they wished from you, or rather what they did not wish. I understand it to be done with good intention and I congratulate the literary community to it.

Concerning the former comets observed by Regiomontanus and the others5 I am expecting that you intend to publish them as soon as possible and you will point out there also my opinion if all comets should be treated as ethereal or if they are partly ethereal and partly elemental.6

It seems to me that you answered completely to what has been up to now blamed on your hypothesis. I also do not find there any contradiction, just opposite everything is mutually in a beautiful agreement. After these hypotheses will be proved - what is missing in the case of Copernicus' hypothesis - i.e. they will indicate accurate positions of stars in the past, present and future times, then it will be finally necessary to decide where the great work which is your goal has to behold light of world. And I do not even doubt, that in this work you will compare with the highest carefulness accurate observations of all times, how many of them only exist, with your own, which are - I resolutely believe in it - the most accurate. And by really divine talent you will erect therefrom a new novel celestial machine.

Welfare to your resolve, the most illustrious man, and do it so that we will use your godlike findings as soon as possible. Despite it is a tedious and - as you write yourself - longstanding task, yet I hope, nay I even hold it, that you have already performed a larger portion of it and that in this time you are dealing with both repeated gathering and ordering of that, what you have already made out, and by assembling of tables from it, rather than by additional proving of your findings. Because the work of your pupils can largely help you, I want to ask you again and again not to let us too long in uncertainty. I wish you with all my heart to live till the age of Nestor. You know, how fallible used to be our hopes and how premature death meets especially heavenly gifted people.7 So circumvent the obstacles and expose to the world this fruit of your genius, perhaps even un-formed. If fate would indulge to you longevity, which is our fervent wish and hope, You could revise again even already published works and so to satisfy also your voice (no doubts that our voice will be satisfied enough by the first edition). You will relieve us thereby of ceaseless fear, that while you would delay for a long time, the whole work would come to nought. I have imposed in you and your hypotheses such big hope, that I dare to claim with certainty, that the real building up of astronomical science is expected from nobody else than from you. You have been endowed beside the strength of godlike talent with so much and such things inevitable to it, you have stand so big expenditures, that in Europe (when say in Europe, I mean in the whole world) there is nobody who could compare with you. There is no soothing in it, I swear before the Lord: both the position I have and the reputation I am trying to save by all means prevent me from doing it with respect to known as well as unknown, and especially to laud a man unknown by sight enough and more than enough. It exceedingly delighted me what you have written at different places to different people on accurate construction and use of instruments necessary for observation. Since I could not satisfy myself yet and because I can not even stand to set eyes on what is not fabricated to perfection, let alone to wish to possess something like that, I lack almost all instruments apart from those, which were constructed merely for pleasure. The Nonnian quadrant often engaged me very hardly, but because it is very difficult, nay even practically impossible to make it, I have thought about another means and I found various, the part of which has been published by the eminent mathematician Christoforus Clavius in his book on sun-dials.8 Finally I found how to construct a quadrant, and because to some learned men it did not seem to be unacceptable, I wanted to send it also to you. However, to confess openly how the matter stands and what you will most probably confirm: all these inventions give in the results less, than they promise at the beginning. I will be pleased to hear your opinion on this my recent finding. Following the book of your N. N. Plagiarist,9 which he dedicated to Paulus Wittich and inscribed it Astronomical basis, and according to his only figure I have created in last days, when I could not devote myself to public service because of bad health, a new teaching on spherical triangles, in which it is very easy to solve by means of tables of sines, tangents and secants all cases of rectangular, as well as oblique triangles without any multiplication or division merely by means of addition and subtraction. I would send it to you as well, if I would not know, that you will the entire matter easily understand by mere look on this figure. From the figure and from the proposition which already many have proved, was built up the whole theory, that the radius vector is the mean proportion between the sinus of straight angle and secants of its complement. What remains: again and again I wish you to be healthy for plenty of years, the most illustrious sir, and I offer to you very friendly all services of sympathies and grace, which can get out from me to you. I persistently ask you to be also henceforth favourably inclined to me, who loves you with all his heart, as you begun to display it by yourself.

Given in Prague, June 28 in the year 1590.

Jacob Kurz of Senftenau

Because there was attached a description of the quadrant mentioned in the letter, I want to enclose it also, because it is clever and it surpasses other discoveries of such type created by Nonnius, as well as by others. Yet however, as openly admits even Mister Kurz himself, in the detailed results there is not that accuracy as promised at the beginning. It agrees with that which is claimed on this topic in the 2nd volume of Progymnasmata, in the 1st part, on p. 461. Namely that apart of the fact that the scales are little inspectional and hardly executable and occasionally easily include some hidden error, there is allowed also the disadvantage , that as the quadrants are closer to the centre, thereby they result smaller. So they are less able to conceive the sub-scales. And if the alhidade itself does not display everywhere, where it is passing, it is not intersecting a line and some point exactly in the middle (what is hard to distinguish), there is worked unnecessarily (to neglect the other disadvantages for now). Therefore our way, which takes place at the very limbus and circumference of quadrant and does not even use too much space and its preparation is also easy, is further more fast and secure. Also because such quadrants do not require a lot of parts, when they can consist of a few only. Yet however I wanted to append here the rather ingenious technique of Mister Kurz, despite that it is not quite suitable for practice. This is namely to ascribe to that notable man his finding and to prevent others from appropriating it (as it is used to do). And also in some way once again after his death to remind gratefully in my mind remembrance of him and to praise his outstanding talent. The description is the following:

Follows the description of scales of quadrant subtly invented by the most illustrious and noble man Jacob Kurz, the imperial vice-chancellor

Inside a quadrant very accurately divided on ninety degrees are inscribed fifty nine other quadrants. And on that, which follows next after the outer quadrant, let is taken the angle of sixty one degrees and that is divided on sixty equal parts; or let is taken the angle of thirty and half degrees and it is divided on thirty equal parts and any of these parts in the first as well as in the second case will be one degree and one minute.

We use only the first of these parts, the others we neglect, as if they have not been on the quadrant, and for this reason it is needed to make this scale hidden or - which we would more advise - the scale is on another quadrant and from there let one of those parts be carried on that which we have completed for this purpose not to mix the parts needed later with the first ones.

From the border of its first part let its semi-diameter is carried on the quadrant and the angle intersected by it is to be divided on sixty equal parts and each of these parts will be one degree or sixty minutes. Semi-diameter of any circle intersects one sixth of the ring, i.e sixty degrees. Next twenty eight of these parts are carried from the border of his angle on the rest of the quadrant and it will be eighty eight identical parts, about which we said, that individually occupy one degree. If you would add to them the first part, about which we said, that it occupies one degree and one minute, there arise eighty nine quadratic and one minute. The rest part, which remains till the end of quadrant, will thus take fifty nine minutes. In the second quadrant, which succeeds next after this, let is taken the angle sixty two degrees and it is divided on sixty equal parts or let the angle of thirty degrees is divided on thirty equal parts and each of these parts will be one degree and two minutes. Also from these parts we use only the first one and the others we neglect. From the border of his first part his semi-diameter is again carried on the quadrant and the angle, which it intersects, is divided on sixty identical parts and twenty eight of them are carried on the rest of quadrant - and again we will have eighty eight whole degrees. If we would add to them the first part, which occupies one degree and two minutes, there arises the angle eighty nine degrees and two minutes and the latest part, which remains till the end of the quadrant, will be fifty eight minutes. For the third quadrant we will take the angle of sixty three degrees from beginning, we will divide it on sixty equal parts or its half on thirty equal parts, and when we will take up the first part and neglect the rest, it will take one degree and three minutes. The rest we perform no-otherwise, than in the case of the first and the second quadrant. For the fourth quadrant it is necessary to take the angle of sixty four degree, for the fifth sixty five degrees and it continues in that way, that it is necessary to take always for the next quadrant angle about one degree larger, until the fifty ninth quadrant, for which must be taken the angle of one hundred nineteen degrees and it must be divided; either this is to be divided on sixty equal parts or the angle fifty nine and half degree on thirty equal parts and each of their parts will take one degree and fifty nine minutes. From the border of his first part, when the others are neglected, it is again necessary to transfer his semi-diameter on the quadrant and the angle intersected by it must be divided on sixty equal parts and twenty eight of these must be transferred on the rest of the quadrant, and again we will have eighty eight whole degrees, to which we will add the first part, and there arise eighty nine degrees and fifty nine minutes and the residual part, which remains at the end of quadrant, will thus have one minute. If the quadrants are divided in this way, to the first quadrant, which we have divided into ninety equal parts, is to be ascribed 0. If the alhidade would pitch on some of the sections of that quadrant, the angle will take exactly and nothing more than a whole degree. To the nearest quadrant succeeding after this one, let is ascribed 1. If the alhidade would pitch on any section of this quadrant, there will be added one minute to the shown degrees.10 To the subsequent quadrant let is ascribed 2, to the next nearby following 3, then 4 and in that way we will go on until the innermost quadrant, to which has to be ascribed 59. If the alhidade would pitch on any section of the inner quadrant, the angle will be fifty nine minutes in addition to the whole degrees.

This quadrant displays in fact five thousand four hundreds portions, i.e. all basic sections which are contained in ninety degrees. It usage is very easy. If the alhidade or the thread of the plumb pitch on some whole section of some of these quadrants there is to be added to the whole degrees shown by the alhidade or the thread of the plumb so many minutes as is ascribed on the side of this quadrant, and this will show the number of degrees and minutes given by the defined angle. For example: the alhidade will pitch on the forty fourth section of the quadrant on both sides of which is ascribed thirty five minutes; the angle determined by the alhidade will thus take forty four whole degrees and in addition to it thirty five minutes.11

1 I.e. to the Rome.
2 Cf. C. Plinius Caecilius Secundus, Epistulae II 3,8: Numquamne legisti Gaditanum quendam Titi Livi nomine gloriaque commotum ad visendum eum ab ultimo terrarum orbe venisse statimque, ut viderat, abisse? - Whether you have never read about the man of Gad, who set out from the outmost parts of the country to see Titus Livius, about whose famous name he had heard so much and who returned back as soon as he saw him?
3 Just Kurz wrote in the year 1590 and send to Tycho together with this letter the privilege of Habsburg monarchy to his treatise De mundi aetherei... phaenomenis, which Tycho published at the beginning of his Progymnasmata (Opera omnia II, 8-10).
4 Lydius lapis, Lydian stone, means touchstone, testing stone. This denotation comes from the Pliniu's treatise Naturalis historia XXXIII, 43: The note about gold and silver is accompanied by description of the stone called `touchstone', occurring formerly only in Tmolus river, as is given by Theofrastos, but nowadays also in another places. Somebody call it `Heraclean', another `Lydian'. ... Experts used these touchstones as files, to determine according to the scratched piece of the ore how much gold, silver or copper it contains.
5 Regiomontanus started observation of comets in 1472 together with Bernhard Walther. After the Regiomontanus' death Walther continued in the investigation of comets in 1491 and 1501.
6 Ethereal means here belonging to the supralunar region of aether and elemental belonging to the sublunar region of elements.
7 Cf. P. Ovidius Naso, Remedia amoris 369-370: Summa petit livor, perflant altissima venti, / summa petunt dextra fulmina missa Iovis.
8 Christophorus Clavius, Fabrica et usus instrumenti ad horologiorum descriptionem peropportuni, Romae 1586. Clavius (by own name Schlussel, 1537-1612) was German mathematician and astronomer, coming from Bamberg. He studied in Coimbra and acted as teacher of mathematics on different Jesuitical institutions. On the call of pope Gregorius XIII he took part in discussion in Rome on the reform of calendar. Clavius' discoveries in trigonometry are formulated in his treatise Astrolabium, Rome 1593. His collectanea (including also Tabulae ad horologiorum constructionem utiles, Romae 1605) were published in the year 1612 in five volumes.
9 By N. N. Plagiarist is meant Nicholas Raimarus Ursus.
10 In this sentence there are missing several words in the Latin original. We emend it in analogy with other text as: ``In quamcunque enim partem hujus quadrantis fiduciae linea inciderit, continebit arcus is ultra gradus ostensos minutum unum."
11 We add a computer simulation of the Kurz's scale. The position of the alhidade according to his example is shown by the oblique disconnected line.

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