# Scripta Clarissimi Mathematici

## Introduction

Johannes Müller (better known as “Regiomontanus” because he lived in Königsberg) was a 15th-Century astronomer, whose patron and student Bernard Walther provided him with instruments and established a printing house for him. When Regiomontanus died in 1476, Walther continued the observations, but never published them. Finally in 1544, their observations were edited and published by Johannes Schöner, as “Scripta Clarissimi Mathematici”. Scanned images of its pages are available at the University of Strassburg.

The printing press was hardly a century old at that time, and the art of printing was not very advanced. Consequently, the book lacks many features we routinely expect today in a technical book: it has neither a table of contents, nor an index, nor consecutively numbered pages. Furthermore, it is full of printing errors — some of which, but not all, are recorded in a double-page spread of Errata at the end of the volume.

## The numbering problem

Some of the pages bear numbers, but they refer to the folios (i.e., the original large sheets of paper that were evidently printed two-up) rather than what we call “pages” today. Worse, they are often out of order; the numbering is so badly screwed up that Schöner says at the end of the Errata that the reader should first correct the numbers of the folios before entering the corrections. The numbering is in fact so completely garbled that Schöner himself got confused, and assigned an incorrect folio number to the penultimate entry!

This brings up the numbering scheme. The folio numbers appear on the right-hand pages, which are regarded as the first (or “recto”) side of a sheet. The back of the sheet — i.e., the following left-hand page, which faces the recto side of the folio with the next higher number — is the second (or “verso”) side. In the Errata, the sides are mentioned as well as the folio number.

Here's a guide to the right folio numbers. Folios 1, 2, 4, and 17 are not numbered; aside from this, everything is OK up to fo. 21. Then things begin to break down:

the folio numbered 20 is really 20
the first numbered 21 is really 21
the   2nd numbered 21 is really 22
the folio numbered 23 is really 23
the folio numbered 24 is really 24
the folio numbered 25 is really 25
the folio numbered 26 is really 26
the folio numbered 27 is really 27
the folio numbered 28 is really 28
the folio numbered 29 is really 29
the folio numbered 30 is really 30
the folio numbered 31 is really 31
the folio numbered 32 is really 32
the folio numbered 33 is really 33
the folio numbered 34 is really 34
the folio numbered 35 is really 35
the folio numbered 36 is really 36
the folio numbered 73 is really 37
the folio numbered 38 is really 38
the folio numbered 39 is really 39
the folio numbered 40 is really 40
the folio numbered 41 is really 41
the folio numbered 42 is really 42
the folio numbered 43 is really 43
the folio numbered 44 is really 44
the folio numbered 45 is really 45
the folio numbered 46 is really 46
the folio numbered 47 is really 47
the folio numbered 48 is really 48
the folio numbered 49 is really 49
the first numbered 50 is really 50
the   2nd numbered 50 is really 51
the folio numbered 52 is really 52
the folio numbered 57 is really 53
the folio numbered 54 is really 54
the folio numbered 59 is really 55
the folio numbered 56 is really 56
the folio numbered 57 is really 57 — the real 57 is the second one
the folio numbered 58 is really 58
the folio numbered 59 is really 59
the folio numbered 60 is really 60
the folio numbered 61 is really 61
the folio numbered 62 is really 62
the folio numbered 63 is really 63
the folio numbered 64 is really 64
the folio numbered 57 is really 65 — this is the 3rd numbered 57!
the   2nd numbered 58 is really 66
the   2nd numbered 59 is really 67
the   2nd numbered 60 is really 68
the folio numbered 69 is really 69
the folio numbered 70 is really 70
the folio numbered 71 is really 71
the folio numbered 72 is really 72
the   2nd numbered 69 is really 73
the   2nd numbered 70 is really 74
the   2nd numbered 71 is really 75
the   2nd numbered 72 is really 76
the folio numbered 73 is really 77 — not to be confused with 37
the folio numbered 78 is really 78
the folio numbered 75 is really 79
the folio numbered 80 is really 80

... and the next 4 folios (81 -84) are numbered correctly, although the final 4 have no numbers at all.

As a result of the confusion at the end, the corrections Schöner says should be applied to fo. 77 actually apply to fo. 78; and the errata for fo. 80 apply to side 2, not side 1.