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:
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.