APPENDIX TO THE HARMONICS

...the mirror, the lathe, and the shapes of triangles: to which you appeal in that passage no differently than a mathematician appeals to his own propositions and theorems. Indeed, in this very tenth Analysis, you wish for them to be considered your diagrams. Furthermore, you admit repeatedly that you have introduced many pictures. Why, then, are you angry? Did I reproach you for these figures as if they were tasteless or a disgrace? Why, then, as if returning a favor, do you list my own figures, which are nevertheless nothing other than diagrams? And what sort of spirit do I recognize in you, who—when you could very easily take indifferent words in a good sense—prefer to take them in a bad one? I compared my diagrams to your pictures; I admitted that my book was not as decorated as yours, nor would it be to the taste of every reader. I excused this defect as a result of my profession, since I act as a mathematician. But from this, you claim I show some kind of boasting. I hate and condemn boasting; but standing on the scholar’s platform, I cannot ignore the distinctions between things. I must invite the student to the study of mathematical disciplines and provide sincere advice as to which book I believe will help them. Let me even now speak with a clearer voice: He who loves the certainty of mathematical disciplines will receive more utility in learning the part of Harmonic Mathematics from my work, The Harmonics, than from that of Robert Fludd original: "Robertus de Fluctibus". But he who desires to feed his mind on mystical philosophy (which is usually handed down through riddles) and his eyes on pictures, will not find what he seeks in my book.

TO ANALYSIS XI.

Here, my dear Robert, you have found some handle for being angry with me: for you hold me to my own words, just as if I had compared my own works to light and all of yours to darkness. But if you can restrain yourself from indignation for a little while, I will demonstrate by explaining my words that not only will the pain you have conceived in your mind (which you testify to with bitter words) be mitigated, but also the reader—if by chance anyone was less attentive to the sense of my words—will in turn lay aside any contempt for your work.

First, I make a distinction in the subject matter. For since there is nothing in the whole world that the vastness of your work does not embrace, I—for my part—do not object to the rest of the parts of your work, supported as they are by the votes of so many learned men whom you cite. But as far as that part of Mathematics called Harmonics The study of ratios and proportions in music, nature, and the cosmos. is concerned: I truly hope that I have demonstrated to readers, through the laborious equipment of my diagrams, an outstanding will and effort to bring things wrapped in obscurity into the light of the intellect. You, in turn, treat Harmonics somewhat differently, and you strip them of quantities (that is, in my judgment, of their own light). For this is the second distinction to be observed in my words: they do not speak of achievement, but of effort. Now, you have already stated above what your purpose is regarding Harmonics: to gather many things into a few, to collect the extracted essence of Harmonics, to reject the power and substance of quantities (as you explain below), and to place what is good in its own little vessel (these are hieroglyphic figures Fludd used complex, symbolic engravings—hieroglyphics—to represent the hidden workings of the universe., which is to say, riddles). For to you, this is to uncover the secret of science and to manifest the hidden: if the internal nature of the Harmonic thing, stripped of its clothing of quantities, is enclosed in a hieroglyphic figure—a nature which, in your judgment, is more suitable so that its power may be seen by the eyes and mind without a circuit of words, as if in a mirror or a riddle. Therefore, when I call your Harmonic riddles (or enigmas) "dark" original: "tenebrosa", I speak from my own judgment and capacity; and I have you as a supporter in this, for you deny that your intention is subject to mathematical demonstrations—without which I am blind. To yourself, you seem to depict everything most brilliantly and to explain them with very significant hieroglyphic figures. Both this seems so to me, and that seems so to you: let us each abound in our own sense; let the reader judge, and the dispute will be settled. Only this remains for me: that I attributed riddles to your goal in Harmonics, and the explanation of obscure things (which is done through words and quantities) to my own effort, without any injury. For I have already proved the former concerning your goal using your own words; and you yourself, in the ninth Analysis, admitted the latter regarding my effort: that I can clarify the harmonies in the heavens and the earth by no better way than the proportion of lengths. And throughout, you reproach me for "verbosity," which is why we usually strive for clarity; whereas you often display pictures in place of the words you reject.

Nor, however, is this the same as if I had said that you hide the mysteries of the ancients, which is your intended...