Nf 



TAIU.I:. 



TABLB. 





born in 154S, anil died in lrt2H. which puts our opinion beyond 

 d--i >it.-. The mistake about Snell teems to hve originate. 1 'with 

 Gerard Viwsius. 



In O' r '- s> > Xic. Raymar, Ursua Dithmarsua, published ' Fundament um 



'im'cum. id eat nov Doctrina Sinuum,' Ac., Strasburg. We 



cannot make out from the description*, whether this work contains 



table* or not. If Knottier'* and Delanibre's descriptions be complete, 



it did not. 



Who published the first English trigonometrical table is a point 

 which we have never seen examined: and we must investigate it in 

 the beat way we can from rather scanty materials. We cam 

 the word 'wf mentioned in the works of Kecorde, nor in the English 

 works of either IHgges, father or son, nor in those of John Dee; nor 

 indeed in any work written in Knglish before lilundeville. except that 

 of Burroughs presently cited. In the ' Alic, seu Scale Math. 

 of Thomas Digges, London, 1573, 4to, trigonometrical processes are 

 required for which allusion ig mode to Copernicus and Kegiomontauus, 

 and the tables of Rheticus are often cited (the ten-minute canon, of 

 l.Vili. In John Dee's ' Parallacticse Commentatiouis Praxeoaque 

 Nucleus quid-mi,' London. 1573, 4to, there are also solution* of 

 triangles, and the tables referred to are those of Ragiomontanns with the 

 radius I;II.HIIII, I < fore mentioned. But neither of these writers makes 

 the smallest allusion to any tables published in England. We have 

 examined the libraries of more than one diligent collector of English 

 works of the I'ith century, without finding anything which at 



- .mi -decided impression that Blundeville * was the real intro- 

 ducer of a complete canon of sines, tangents, and secants. 



Blundeville's ' Exercises,' London (1534), 4to (it is said sometimes 

 that 1S97 is the date of the first edition, but incorrectly ; the fourth 

 is of 101 3>, were commenced, as he informs us, about seven years 

 before. He alludes to Kegiomontanus, Copernicus, and ( 

 whom he took his tables. And he informs us that Hegiomontanus is 

 in folio, and that Clavius is in quarto, and published in 1586, at Koine. 

 W,- rely much on this in our conclusion that his were the first tables : 

 for to mention the form of a book, or the date of publication, is very 

 rare with the writers of his time ; and it is most likely that so precise 

 a person would have noticed any previous work of the same kind in 

 his own country. The tables, being copies of Clavius, have already 

 been described. These ' Exercises ' went through seven editions at 

 least: the seventh, now before us, has the tables corrected from 

 Pitiscrs, by KoWt Hartwell, the editor; it is London, 1Mb, -Ito. 



It must be noticed, however, that though Blundeville gave the first 

 English canon complete, a table of sines unly had been printed four 

 years before. It is at the end of the ' Horologiographia, the art of 

 Dialling,' by Thomas Fale, London, 1593, 4to (reprinted t in lti.1^1. 

 The sines are to minutes with a radius of 100,000. This then is the 

 earliest table, but it is of sines only. We have seen that Diggea used 

 sines, but he is a Latin writer, and refers to a foreign table. Perhaps 

 the first writer who iwrf them in English (but still with foreign 

 is the well-known W. Burroughs, in his 'Discourse on the Variations 

 of the Compasse,' published in (1581). In the preface he apologises 

 for introducing rules " wrought by the doctrine of signes and triangles, 

 which may seem strange in our English-Tongue," and all he gives on 

 tables is in the following passage : " In these examples 1 have used 

 the abridged table of 100,000 the whole sine, which though it give 

 some ease in the working, yet it is not so exact as that of 10,i 

 of Erafiiiii* /.'..'/.../// ii, 1. Unto the which, with his Vanon fm'tiiii/ia, 

 :.ibleto the same, if the thh. | the Ifaptbenuvn w. iv 



annexed, wee should have an entire Table for the Doctrine, of Triangles, 

 that might worthily bee called The- TuM< <// 7V./... Which thin-. 

 though (jtuiyiuf ./ , have well begunue, and framed it 



ordeily, from ten Minutes to ten : yet is it left very rawly, for such as 

 desire the exact truth of things. 1 have therefore for mine owr 

 and use, Calculated the complement of this Table, and aluioste ended 

 it, for the whole Quadrant, from minute to minute : which if in the 

 mean time before I have finished, 1 shall not finds it extent ' 

 other, I will publish it for the cpmmoilitie of all |uo|] as shall have 

 occasion to use the same fur navigation and cosmographie." lint this 

 table was never published, and accordingly the editor of the edition of 

 1614 refers the reader to Ralph Handson'a translation of I'itiscus, and 

 the very tobies of that work are annexed to the end 'pies at 



on of 1614. They are tables to every minute, and 

 toja radius oi IIHI.IIIMP. The table is semi-ijuadrantal, and the com- 

 plementals are joined in contiguous columns, without any heading by 

 which further than 45 could be guessed at. We cannot describe the 

 first edition of Handson's work, having only seen the second, which is 

 London, 163U, 4tp ; at least the tablet are so dated, though the worl 

 has no date. (Wilson, in the preface to his Navigation, 



This Is the name as the Blundevillc who wrote on Horsemanship. In 184C, 

 a patent for a hurimhoc wa upset in Chancery, upon proof that Blundoville 

 bad described it before 1600. 



f 'ihrnt ii to sny, furni.bcd with a new title-page : beyond a doubt the type 

 ii of the previous centuiy. This, we nnd, wo not an uncommon pr< 

 the middle of the 1 7th Cfnturj-, in England. We suppote tbul the civil troubles, 

 which operated against the production of all but theology or politic?, threw the 

 bookseller* back on their old stocks, which they then replaced with new title- 

 page*, defacing the 1/th century with some of the worst specimens of the 

 irregular blick letter of the 16th. 



was in 1614.) In 180!>, John Speidel, afterwards well known in ill- 

 history of logarithms, began bis career by publishing, in 

 ' Certaine verie necesaarie and profitable m.|\..\ ,' 



Sinea, Tangents, and Secants, &c.' This tract of sixteen pages contains 

 a canon to every ten minutes, and to a radiua 1000, with some 

 aubsidiary to astronomy. 



In lilin, Arthur lioptmi published ' Baculum Geodicticm 

 Viaticum, or the L!eod;ctical I Statl'c,' London, 4to. The .-. 

 of this ia called ' Trigonometria, containing Lon^im.-tiii, and Alti- 

 raetria, performed by Synnieall supputatiuii, with a (.anon for the 



; on of tryangles." The canon (from Pitiscus) is 00 

 . minutes and to a radius of 100,000. Peculiar i 



tding by which the tine, tangent, secant of the complement, or 

 defect from 90, arc al.-o made to belong to the excess above 90; 

 thus at 10 the aine, tangent, and secant of 80 are made to be those 

 of 100. 



The history of the rest of the works of Rheticus was, till lateh . 

 inaccurately told, and there ia atill some confusion about it. 

 Rbeticua had published his ten-minut .anon, already notic. 

 1551, he was occupied till his death in 15"ti, in what is, beyond a 

 doubt, the most laborious work of calculation that any on n. 

 undertook : a complete trigonometrical canon to every ten si 

 and to ten places or decimals, sines to every ten seconds, and to 

 decimals, with the first and last degree to every second, a 

 and secants to every minute, and to fifteen decimals. It is 

 remembered that he wanted the abbreviations which might hav 

 introduced, if he had known what Vieta had don.-. th, he 



had finished this work, within a mere trifle: what little reman 

 do, was done by his pupil Valentine Otho, and part of it w 

 atNeustadt* in the Palatinate, 151MI, in folio (sometime-* bound in 

 two volumes, from its thickness). The title of the h..ok, whie 

 published at the expense of the Emperor Maximilian, is Opus I'ala 

 timini de Triangulis a Georgio Joachimo Rhetico cxrptum : L. Valen- 

 tinus Otho Priucipis Palatina Frederici IV. Electoris Mathcmatiuus con- 

 suminavit.' , The contents are (after prefaces) three books de /' 



. on the construction of the Canon, by Rheticus; one bo 

 plane triangles, and four books on ri'jlii-itij!(d spherical triangles, by 

 the same ; live books on oblique-angled spherical triangles by the . 

 Otho ; three subsidiary astronomical tables called mettoracopia ; the 

 great table, in 540 folio pages, giving, under the titles , 

 the sines, tangents, and secants, for every ten seconds, with a radiua 



'.on, 1,000, or, as we should now say, to ten places of dec'. 

 a list of errata ; and lastly, a second table of cotangents and cos. 

 for the first half of the quadrant, to every ten seconds as befoi 

 to a radiua of 10,000,000. The appearance of the last table is merely 

 the editor's want of judgment; it is clearly nothing but a previous 

 attempt, made before the larger plan was resolved on, and is much less 

 accurate than the great table to ten places. 



Within a short time after the ' Opus Palatinum ' was published, it was 

 found (by whom or how we are not told) that the tangents and .-. 

 towards the end of the quadrant became more and more erroneous, 

 and at the extreme end were very erroneous indeed. All persons wild 

 know anything of trigonometry are aware that, to calculate the tangent 

 or secant of an angle near to 90 true to any number of decimal 

 requires that the cosine should be calculated to a greater number of 

 places. Rheticua seems to have foreseen this, and to have pi.. 

 iinea true to a larger number of places than those which wei 

 lished. When the defect was discovered, the advisers of the J . 

 Palatine, Frederick IV., to whom the work was dedicated by 

 caused him to intrust the superintendence of the corrections to IJar- 

 tholomew Pitiscus of Uriinenberg, in Silesia, who had been his own 

 teacher, and who was still in his service as chaplain : we suppose this 

 meana that Pitiscus himself was the adviser. I'itiscus applied to 

 Otho, then an old man, for the larger tables of sines which III 

 was known to have calculated : Otho was never able to find them 

 at his death they were found among his papers. Pitiscus accordingly 

 made twu publications ; but so confused are the statements respecting 

 them, that some of our readers may almost doubt the fact. Tin 

 publications were as follows : 1. He corrected all that part of the 

 able of the ' Opus Palatinum' in which the tan-eni-. an. I aecan 

 sensibly erroneous, being the first 8 In- reprinted, and 



joined his reprint to the 540 86, or 454 remaining j 

 able. He then cut away all the J-\i/:/ ..*, the books on 



triangles, the Ifftfortitoopla, and the small table of co; .. and 



added to his own 86 pages and Otho's l.> I a short des. i ipt ion, or COM- 

 mvnefactio, as he calls it. Thia of course gives a thin folio, lint we 

 collect from Delanibre's account of Prony'a copy, that besides this, 

 ;here were such things aa complete copies of the ' Opus Palatinum,' with 

 the 86 -CS substituted for the incorrect ones. And we 



that to these the separate title of the < 



appended, beiup printed only for the separated table. For Prony, 

 Uelambre, and all the rest of the French savans (to whom the subject 

 was particularly interesting, on account of its connection wit. 

 Tahles .In Cadastre,' then pieparingi missed the date of the corn 

 which nevertheless appears on c title-page of the c/.. . 



F Weidler, copied by Montucla, (jives llei.lclbrrg, 15U4 ; nnd Lulandc i 



s them with fact by tiikiii: In l.o l.iitin lor Heidelberg! The 



istadt here mentioned Is now part of B.ivarin, lai. 411 , long, 11. 



