# The Construction of the Wonderful Canon of Logarithms/Appendix to Catalogue

APPENDIX.
In the preparation of the foregoing Catalogue, several works by other Authors were met with which have considerable interest from their connection with the works of Napier. It seemed desirable to preserve a record of them, and they are accordingly given below, with such particulars as were noted at the time.
Napiers| Narration:|Or,|An Epitome|Of|His Booke On The|Revelation.|Wherein are divers Misteries disclosed,|touching the foure Beasts, seven Vials, seven Trumpets,|seven Thunders, and seven Angels, as also a discovery of|Antichrist: together with very probable conjectures|touching the the time of his destruction, and|the end of the World.|A Subject very seasonable for these last Times.|
Revel. 22. 12. And behold I come shortly, and my reward is with me, to give to every man
London,|Printed by R. O. and G. D. for Giles Calvert, 1641.|
'4°. Sizeinches. A1$^1$, Title.A1$^2$, blank.A2$^2$–C3$^2$, 20 pages, “Napier’s Narration Or An Epitome of his Booke on the Revelation.” C4, 2 pages, blank.
Signatures. A, B, and C in fours = 12 leaves.
Paging. 2 + 20 + 2 = 24 pages, not numbered.
Errors in Signatures. C2 numbered in error C3.
This tract is written in the form of a dialogue, wherein Rollock is made the scholar and Napier the master: see Memoirs, p. 175.
Libraries. Brit. Mus. Lon.; Bodl. Oxf.;
​The bloody Almanack :|To which England is directed, to foreknow what shall|come to passe, by that famous Astrologer, M. John Booker.|Being a perfect Abstract of the Prophecies proved out of Scripture,|By the noble Napier, Lord of Marchistoun in Scotland.|
London| Printed for Anthony Vincent, and are to be sold in the Old-Baily. 1643.|
[With large woodcut in centre of page containing symbolical designs.]
4°. Sizeinches.A1$^1$, Title.A2$^1$, blank.A2$^1$–A4$^2$, pp. 1–6, “The bloody Almanack,” containing “I. Concerning the opening of the seven Seales mentioned Revel. 6.”; “II. Concerning the seven Trumpets mentioned chap. 8 & 9.”; “III. Concerning the seven Angels mentioned Rev. 14.”; “IIII. Concerning the Symboll of the Sabboth.”; “V. Concerning the Prophesie of Elias.”; “VI. Concerning the Prophecie of Daniel.”; “VII. Concerning Christ’s owne saying.”
Signature. A in 4 = 4 leaves.
Paging. 2 + 6 numbered = 8 pages.
Libraries. Brit. Mus. Lon.;
Another Edition.
The bloody Almanack:|To which England is directed .......|Bythe noble Napier, Lord of Marchistoun in Scotland.|With Additions.|
London|Printed for Anthony Vincent, and are to be sold in the Old-Baily.1643.|
[The printing round the woodcut is slightly altered.]
The additions are on A1$^2$ “A Table.…” and “M. J. Booker his Verses.…”, also on A4$^2$ at the end an added Note.
Libraries. Brit. Mus. Lon.;
A|Bloody Almanack|Foretelling|many certaine predictions which shall come to|passe this present yeare 1647.|With a calculation concerning the time of the day|of Judgement, drawne out and published by that famous|Astrologer.|The Lord Napier of Marcheston.|
[With symbolical woodcut surrounded by the signs and names of the zodiac.]
​4°. Sizeinches.A1$^1$, Title. A1$^2$–A2$^2$, 3 pages, Astrological prediction of events “In January,” “In February,” etc.A3$^1$–A4$^2$, 4 pages, “I. Concerning the seaven Angels mentioned Rev. 14.”; “II. Concerning the Symboll of the Sabbath.”; “III. Concerning the Prophesy of Elias.”; “IV. Concerning the Prophecie of Daniel.”; “V. Concerning Christ’s own saying.”; these contain the same matter as in the Almanack of 1643, but the first two subjects there treated of are here omitted.
Signature. A in 4 = 4 leaves.
Paging. 8 pages not numbered.
Libraries. Brit. Mus, Lon.; Bodl. Oxf.;
Le|Sommaire|Des Secrets De|l’Apocalypse, svy-|uant l’ordre des Chapitres.|Le tout conforme aux passages de l’Escriture saincte, tant|de la Doctrine des Prophetes, que des Apostres.|Par le Sieur de Perrieres Varin. |
Heureux sur qui le Soleil d’intelli-|gence se leue.|
Iouxte la coppie imprimee à Rouen.|
A Paris,|Chez Abraham le Feure, ruë sainct Ger-|main de Lauxerrois.|M.C.D.X.|Auec Priuilege du Roy.|
8°. Size 6 1/2 × 4 inches. A1$^2$, Title. A1$^1$, blank.A2{sup, pp. 3 & 4. Dedication “A Tres-havt Et Tres-pvissant Seignevr, Messire Guillaume de Hautemer, sieur de Feruaques,.… & Baron de Manny;.…”A3$^1$–H3$^2$, pp. 5–62, “Les Secretz De L’Apocalypse ouuerts et mis au iour.”H4$^1$ [p. 63], “Approbation,” dated 20 June 1609.H4$^2$ [p. 64], “Extraict du Priuilege du Roy,” dated 27 March 1610.}}
Signatures. A to H in fours = 32 leaves.
Paging. 64 numbered (except on first two and last two) = 64 pages.
From the title-page it would appear that a previous edition had been published at Rouen. The work is written to confute Napier’s interpretation of the Apocalypse, and commences thus:—
Depvis quatre ou cing ans, a esté veu vn liure intitulé, L’ouuerture de l’Apocalypse, mis en lumiere par Napeyr Escossois, duquel n’ay voulu publier les erreurs, aduerty que ses partisans mesme le desauouēt, cōme plein de mensonges & impostures...... Croy certainement qu’en son œuure Sathan a voulu iouër sa reste; Et voyant son temps si prés, nous enuoyer par ce docteur ses harmonyes Pythonissiennes, cauteleusement douces, & à la verité pleines d’attrait, pour nous pyper.
Libraries. Un. Ed.;
​Le|Desabvsement,|Svr Le Brvit Qvi Covrt|de la prochaine Consommation|des Siecles, fin du Monde, & du|Iour du Iugement Vniuersel.|Contre Perrieres Varin, qui|assigne ce Iour en Pannée 1666.|Et Napier Escossois, qui le met en|l’année 1688.| Par le Sieur F. De Covrcelles.|
A Rouen,|Par Lavrens Mavrry, ruë neuve|S. Lo, à l’imprimerie du Louvre.|M. DC. LXV.|Avec Permission.|
12°.
Libraries. Brit. Mus. Lon.;
Aureum|Johannis Woltheri Peinensis Saxonis:|Das ist:| Gviden Arch, Da-|rinn der wahre Verstand vnd Einhalt der| wichtigen Geheimnussen, Wörter vnd Zahlen, in der | Offenbahrung Johannis, vnd im Propheten Daniel, reichlich|vnd über- flüssig gefunden wird, Wie dann auch eine bewerthe Prob aller|Propositionen, vnd auszführliche Wiederlegung, der vermeynten lang-|gewünscheten Auszlegung über diese Offenbarung Johannis, desz Treffli-|chen Schottländischen Theologi, Herrn Johannis Napeiri, durch|die Historien vnd Geschichten der zeit erklaret|vnd angezeigt. Mehr wird auch darinn vor Augen gelegt|vnd dargestellt, wie übel vnd böszlich M. Paulus Na-|gelius mit dem Propheten Daniel vnd der Offenbahrung Jo-|hannis vmbgehe, vnd was von seiner, vnd der andern Newen|Rosencreutzbrüder Astronomia gratiæ oder Apocaly-|ptica zu halten sey.|Letzlich werden auch erörtert H. Napeiri, Wolffgan-|gi Mäyers, Leons de Dromna, vnd anderer Calvinisten|grobe Jrrthumbe von der Rechtfertigung eines armen|Sünders, auch anderen Glaubens Articuln|Nebenst auch einem kurtzen Discurs von den Kirchen-|Ceremonien, &c.|
Psal. 94.|Recht musz doch recht bleiben, vnd dem werden alle fromme Hertzen zufallen,|
Gedruckt zu Rostock, durch Mauritz Sachsen, In vorlegung|Johan Hallervordes Buchhändlers daselbst. 1623.|
[Printed in black and red.]
​4°. Size 6 × 4 inches.Black letter. A1$^1$, Title-page. A1$^2$, blank.A2$^1$–B3$^2$, 11 pages, Dedication to Kurfürst Georg Wilhelm Markgraf von Brandenburg, signed “Datum Liechtenhagen den 15 Octobris des 1621. Jahres......E. Churf. Durchl. Gehorsamer Vnterthan Johannes Woltherus Pfarrherr daselbst.”On B3$^2$ is the title of the German translation of ‘A plaine discovery,’ printed at Frankfurt in 1615.B4$^1$–Nn3$^2$, pp. 1–272, The work itself [see note].On Nn4$^1$ is printed “Gedruckt vu Rostock|durch Moritz Sachsen,|Im Jahr Christi|1623.|” Nn4$^2$, blank.
Signatures. A to Z and Aa to Nn in fours = 144 leaves.
Paging. 14 + 272 numbered + 2 = 288 pages.
Johann Wolther, the Pastor of Liechtenhagen, was a zealous Lutheran, and adherent of the Augsburg Confession. In his work he reprints in full the 36 propositions of Napier’s First treatise as given in the Frankfurt edition of 1615, pp. 1–122, omitting the ‘Beschluz,’ p. 123. To each proposition is appended a refutation of the same. These refutations, being much longer than the propositions, form the bulk of the book.
Libraries. Un. Breslau;
Künstliche Rechenstablein|zu vortheilhafftiger vnd leichter ma-|nifaltigung, Theilungwie nicht|weniger|Auszziehung der gevierdten vnd Cubi-|schen Wurtzeln, allen Rechenmeistern, In-|genieuren, Bawmeistern, vnd Land-|messern, vber die masz dienlich. | Erstlich 1617. In lateinischer Sprach durch Herrn Johan Nepern, Freyherrn in Schottlandt,|beschrieben, nacher ausz anleytung, desz hochgelehrten|weitberühmbten Herrn v. Bayrn durch Frantz Keszlern zu Werck gericht. In Kurtz verfast, vnd zum Truck gefertigt.|
Gedruckt zu Straszburg bey Niclaus|Myriot, In verlegung Jacob von der Heyden Chal-|cographum| Anno MDCXVIII.|
4°. Sizeinches. Black letter.
Libraries. Stadt. Frankfurt; K. Hof u. Staats München;
Rhabdologia|Neperiana.|Das ist,|Newe, vnd sehr leichte|art durch etliche Stäbichen allerhand Zah-|len ohne mühe, vnd ​hergegen gar gewisz, zu Multiplici-|ren vnd zu dividiren, auch die Regulam Detri, vnd beyderley ins|gemein vbliche Radices zu extrahirn: ohne allen brauch|des sonsten vb-vnnd nützlichen|Ein mahl Eins,|Alsz in dem man sich leichtlich|verstossen kan,|Erstlich erfunden durch einen vornehmen Schottlän-|dischen Freyherrn Herrn Johannem Neperum|Herrn zu Merchiston &c.|Anjtzo aber auffs kürtzeste, alsz jmmer müglich gewesen,|nach vorhergehenden gnugsamen Probstücken|ins Deutsche vbergesetzt,|Durch|M. Benjaminem Ursinum, Churf. Bran-|denburgischen Mathematicum.|Cum Gratia Et Privilegio.|
Gedruckt zum Berlin im Grawen Kloster, durch George Rungen,|Im Jahre Christi 1623.|
4°. Size 6 1/4 × 4 1/2 inches. A1$^1$, Title.A1$^2$, blank.A3$^2$–C4$^1$, 3 pages, “Vorrede an den guthertzigen Leser.”A3$^2$–C4$^1$, 18 pages, “Von der Stäbelrechnung,” containing Cap. I. “Von beschreibung und gebrauch der Stäblichen ins gemein.”; Cap.II. “Wie das Multipliciren mit hülff der Stäbichen verrichtet werde.”; Cap III. “Wie das Dividiren anzustellen sey.”; Cap IV. “Von erfindung einer jeden Zahlen quadrat Wurtzel.”; Cap. V. “Wie man mit hülffe des Blätichen Pro Cubica, vnd der Stäbichen einer jedern Zahl radicem cubicam erfinden solle.”C4$^2$, “Der Leser wisse, wo er der mühe die Stäbichen auffzutragen, wil vberhaben sein: das solche zierlich in einem subtilen Kästichen, aller notturff nach zugerichtet zubekommen sein. Vnd zufinden bey Martin Guthen, Buchhändlern zu Cölln an der Spree.”
Signatures. A to C in fours = 12 leaves.
Paging. 24 pages not numbered. Facing A3$^2$ on a folding sheet is a diagram of the rods.
Libraries. Brit. Mus. Lon.; K6n. Berlin; Stadt. Breslau; Nat. Paris;
Another Edition.
Gedruckt im Jahr Christi,|Anno 1630.|
Libraries. Stadt. Zurich;
Manvale|Arithmeticæ & Geometriæ Practice :| In het welcke|Beneffens de Stock-rekeninghe ofte|Rhabdologia J. Napperi cortelick eñ duydelic t’ ge-|ne den Landmeters eñ Ingenieurs, nopende ’t Land-|meten en Sterckten-bouwen nootwendich is, ​wort|geleert ende exemplaerlick aenghewesen.|Op een nieu verrijckt met een nieuwe inventie on alle ronde va-|ten hare wannigheden af te pegelen.|Door|Adrianum Metium. Med. D. & Ma-|thes. Profess. ordinar. binnen Franeker.|
Tot Amsterdam,|By Henderick Laurentsz, Boeckvercooper op ’t|Water, int Schryfboeck, Anno 1634.|
8°. Sizeinches.
Paging. 16 + 246 numbered + 8.
Another Edition.
Gedruckt by Ulderick Balck, Ordi-|naris Landschaps ende Academiz Boecke-|Drucker. Anno 1646.|
Paging. 8 + 377 numbered + 11.
These two editions are catalogued by D. Bierens de Hann in his papers entitled ‘Bouwstoffen voor de Geschiedenis der Wi-en Natuurkundige Wetenschappen in de Nederlanden,’ communicated to the Amsterdam Academy—Verslag. xii., 1878 (Natuurk.), p. 19.
The Art of|Numbring|By|Speaking-Rods:|Vulgarly termed|Nepeir’s Bones.|By which|The most difficult Parts of| Arithmetick,|As Multiplication, Division, and Ex-|tracting of Roots both Square|and Cube,|Are performed with incredible Cele-|rity and Exactness (without any|charge to the Memory) by Addi-|tion and Substraction only.||Published by W. L. ||
London;|Printed for G. Sawbridge, and are to be sold|at his House on Clerkenwell-Green, 1667.|
12°, Size 42 × 23 inches.A1, blank?A2$^1$, Title-page.A6$^2$, blank. A3$^1$–A6$^1$, 7 pages, “The Argument To The Reader.”A6$^2$, blank. After A6$^2$ on a folding sheet is a diagram of the rods. B1$^2$–E7$^2$, pp. 1–86, The Work. E8$^1$, “Errata.” E8$^2$–E9$^2$, 3 pages, Advertisements.E10$^1$–E12$^2$, 6 pages, blank?
Signatures. A in six + B to E in twelves = 54 leaves.
Paging. 12 + 86 numbered + 10 = 108 pages.
The author was William Leybourn, and the work contains a short ​description of the rods, with examples of their use in multiplication, division, and the extraction of square and cube roots.
Libraries. Un. Ed.; Brit. Mus. Lon. (2); Lambeth Pal. Lon.;
Another Edition.
London, printed by T. B. for H. Sawbridge, at the|Bible on Ludgate-Hill. 1685.|
Libraries. Un. Ab.; Brit. Mus. Lon.;
Nepper’s Rechenstäbchen, als Hülfsmittel bei d. Multiplication u. Division d. Zahlen- u. Decimalbrüche; hrsgg. v. F. A. Netto. Mit 100 Rechenstäbchen, Dresd. 1815. Arnold. 18g.
{{fine|This entry is copied from C. G. Kayser’s Vollstandiges Bücher-Lexicon (1750-1832), published at Leipsic in 1835. The work apparently treats of ‘Napier’s Bones.’
Traité De La|Trigonometrie,|Povr Resovdre Tovs|Triangles Rectilignes|Et Spheriqves.|Avec Les Demonstrations Des|deux celebres Propositions du-Baron de Merchiston,|non encores demonstrees.|Dediée|A Messire Robert Kar, Comte| d’Ancrame, Gentil-homme de la Chambre|du Roy de la Grand’ Bretagne.|
A Paris,|Chez Nicolas et Iean de la Coste, au|mont S. Hilaire, à l’Escu de Bretagne, & en leur|boutique à la petite porte du Palais|deuant les Augustins.|M. DC. XXXVI.|Avec Privilege Du Roy.|
8°. Size 6 1/8 × 3 7/8 inches. a1$^1$,–ĩ4?, 20 pages, Preliminary matter. a1–p2$^2$, pp. 1–116, “Des Triangles Rectilignes.”A1$^1$–Y4$^1$, pp. 1–193 [175] “Des Triangles Spheriqves.”Y4$^2$, woodcut.
In the first part, on a folio sheet facing p. 68, is a table of ‘Racines de 10’ and of their logarithms.
Paging. 20 + 116 numbered + (193 - 18 for error =) 175 numbered + 1 = 312 pages.
Signatures. ã in 4, ẽ in 2 & i in 4 + a to o in 4 & p in 2 + A to Y in 4 = 156 leaves.
​Errors in Paging. In first part none of consequence. In second part 168 numbered 186, and so to the end, thus making an error in excess of 18.
Permission to print the work was given on 5th April 1635. The Dedication is signed by the Author ‘Iacobvs Hvmivs, Theagrius Scotus.’ On the last page (p. 116) of the first part will be found the passage relating to Napier’s burial-place, &c., part of which is quoted at p. 426 of the Memoirs. The two celebrated propositions by Napier are Nos. 117 & 120 of the second part.
Libraries, Adv. Ed.; Un. Ed.; Roy. Soc. Lon.;
Primvs Liber|Tabvlarvm Directionvm.|Discentivm Prima Elemen-|ta Astronomiz necessarius &|utilissimus.|His Insertvs Est Canon|fecundus ad singula scrupula qua-|drantis propagatus.|Item Nova Tabvla Clima-|tum & Parallelorum, item umbrarum.|Appendix Canonvm Secvndi| Libri Directionum, qui in Regiomontani|opere desiderantur.|Avtore Erasmo|Rheinholdo Salueldensi|Cum gratia & priuilegio Czsaree &|Regiz Maiestatis. |
Tvbinge Apvd Hære|des Vlrici Morhardi. Anno|M.D. LIIII.|
[Printed in black and red.]
4°. Size 8 x 5 3/4 inches.
In describing the formation of the Logarithmic Table, in section 59 of the Constructio, Napier says that Reinhold’s common table of sines (or any other more exact) will supply the values for filling in the natural sines in columns 2 and 6, and the table of sines in this work (“Canon Sinvvm Vel Semissivm Rectarvm In Circvlo Svbtensarvm.”, fol 114), was probably the one he made use of.
Libraries. Trin. Col. Dub.;
Benjaminis Ursini|Sprottavi Silesi|In Electorali Brandenburgico Gymnasio|Vallis Joachimicæ,|Cursus| Mathematici|Practici|Volumen Primum|continens| Illustr. & Generosi DN.| ​DN. Johannis Neperi|Baronis Merchistonij &c.| Scoti.|Trigonometriam Loga-|rithmicam|Usibus discentium accomoda-|tam.|Cum Gratia Et Privilegio.|
Typisq. exscriptam|Coloniæ sumtibus Martini Guthij,|Anno CIƆ IƆ XVIII.|
[Note. Colonia = Köln a.d. Spree = Berlin.]
8°. Size 4 7/8 x 3 inches. A1$^1$, Title.A1$^2$–A3$^2$, 5 pages, Dedication to “Illustri et generoso domino, Dn. Abrahamo lib. Baroni et Burggravio de Dohna……” signed “in Valle nostra Ioachimica XVI, Kal. Jun. anni seculi hujus XVII. T. Illustr. Generos. humilimè addictus Cliens Benjamin Ursinus.”A4$^1$–C7$^2$, 40 pages, “Trigonometriæ Logarithmicæ J. Neperi, &c.”C8, 2 pages, blank. Aa1$^1$, The title, “Tabula Propor-|tionalis|Sequenti|Canoni|Logarithmo-|rum Inser-|viens.|” Aa1$^2$–Aa5$^1$, 8 pages, The Table. Aas5$^2$–Aa7$^2$, 5 pages, “Usus precedentis tabulæ.”|Aa8, 2 pages, blank.Bb1$^1$, The title, “J. Neperi|Baronis Mer-|chistoniz, Sco-|ti, &c.|Mirificus|Canon Logarith-|morum.”Bb1$^2$–Gg6$^1$, 90 pages, The Canon to two places less than that of 1614.Gg6$^2$–Hh2$^2$, 9 pages, “Lectori Benevolo,” [errata.] The work should have ended on Hh1$^2$, but through an error in printing, the two pages, Hh1$^2$ and Hh2$^1$, have been left blank.
Signatures. A to C and Aa to Gg in eights + Hh in two = 82 leaves.
Paging. 48 + 16 + 91 + 9 = 164 pages not numbered.
Napier’s Canon of 1614 is here reprinted, but is shortened two places.
Libraries. Brit. Mus. Lon.; Stadt. Breslau;
Another Edition.
Colonize, Martinus Guthius, 1619.
Libraries. Bodl. Oxf.; Un. Camb.; Nat. Paris;
The First Edition
is stated to have been published in 1617, which is no doubt correct, as the Dedication is dated 17th May 1617.
Beni. Ursini|Mathematici Electora-|lis Brandenburgici| Trigonometria|cum magno|Logarithmor.|Canone|Cum Privilegio| ​Coloniæ|Sumptib. M. Guttij, tipys|G. Rungij descripta.|CIƆ IƆC XXV.|
[The above is engraved on a half-open door, forming the centre of a title-page elaborately engraved by Petrus Rollos.]
4°. Size 7 5/8 x 5 3/4 inches.):( 1$^1$, Title.):( 1$^2$, blank.):( 2$^1$– ):( 4$^2$, 6 pages, Dedication to Dn. Georgio Wilhelmo Marchioni Brandenburgico, dated 1624. A1$^1$–Ll4$^2$, pp. 1–272. Trigonometria, in three books. Liber I., “De Triangulis, eorumg. affectionibus.” ; Sectio Prior, “De Triangulis Planis.”; Sectio Posterior, “De Triangulis Spharicis.” . Liber II., “De Constructione Canonis Triangulorum; ejusg. usu in genere.”; Sectio I., “De Constructione Canonis Sinuum.”; Sectio II., “De Constructione Tabule Logarithmorum.” ; Sectio III., “De usu Canonis Logarithmorum in genere.” . Liber III., “De Usu Canonis Logarithmorum in utrag. Trigonometriâ.”; Sectio I., “De Mensuratione Triangulorum Planorum sive Rectilineorum.” ; Sectio II., “De Trigonometria Sphericorum.”
Signatures. ):( and A to Z and Aa to Ll in fours = 140 leaves.
Paging. 8 + 272 numbered = 280 pages.
Benjaminis Ursini|Sprottavi Silesi| Mathematici Electoralis Brandenburgici|Magnvs Canon|Triangulorum|Logarithmicvs;|Ex Voto & Consilio|Illustr. Neperi, p. m.|novissimo,|Et Sinu toto 100000000. ad scrupulor,|secundor. decadas|usq’.|Vigili studio & pertinaci industriâ|diductus.|
Keppler. Harmonic. Lib. iv. cap, vii. p. 168.—[followed by extract of 8 lines.]
Coloniæ,|Typis Georgij Rungij, impensis & sumtibus Martini Guttij|Bibliopolæ, Anno M. DC. XXIV.|
A1$^1$, Title.A1$^2$, blank.A2$^1$–Lll$^2$, The Table occupying 450 pages. Lll3$^1$, “Emendanda in Canone,” 35 lines.On Lll3$^2$ is printed “Berolini,|Excudebat Georgius Rungius Typographus,|impensis & sumtibus Martini Guttij|Bibliopolæ Coloniensis.| Anno clɔ Icɔ xxiv.|”.Lll4, blank.
Signatures. A to Z and Aa to Zz and Aaa to Lll in fours = 228 leaves.
Paging. 2 + 450 + 4 = 456 pages not numbered.
Colonia, the place of publication, is Köln a. d. Spree or Berlin.
The second and third books of the Trigonometria deal with the subjects treated of in Napier’s Descriptio and Constructio, these works being largely made use of by Ursinus, who speaks of Napier as a Mathematician without equal (see p. 131, l. 5). The references in the text are to the Lyons edition of 1620 (see p. 178).
The Magnus Canon contains the logarithms of sines for every 10″ in the quadrant. They are arranged in a similar way, and are of the same kind as those in Napier’s Canon of 1614; but are carried one place ​
| | | Grad. 0. | Grad. 0. | Grad. 0. | + | + | − | − | − | − | − | − | − | − |
| M.S. | M.S. | Sinus | D. | Logarith. | D. | Different. | Different. | D. | Logarith. | D. | Sinus | D. | | |
| 0 | 0 | 50000000 | 99 98 | 69314718 | 97 96 95 | 54930614 | 54930614 | 97 95 | 14384104 | 00 99 2800 | 86602540 | | 60 | |
| | 10 | 04199 | 99 98 | 06321 | 97 96 95 | 19417 | 19417 | 97 95 | 86904 | 00 99 2800 | 00116 | 24 | 50 | |
| | 20 | 08397 | 99 98 | 69297925 | 97 96 95 | 08222 | 08222 | 97 95 | 89703 | 00 99 2800 | 86597692 | | 40 | |
| | 30 | 12595 | 99 98 | 89530 | 97 96 95 | 54897027 | 54897027 | | 92503 | 00 99 2800 | 95267 | 2425 | 30 | |
| | 40 | 16794 | 99 98 | 81136 | 94 93 92 | 85833 | 85833 | 94 | 95303 | 00 99 2800 | 92842 | 2425 | 20 | |
| | 50 | 20992 | 99 98 | 72743 | 94 93 92 | 74640 | 74640 | 93 | 98103 | 01 | 90417 | 2425 | 10 | |
| 1 | 0 | 25190 | 97 98 | 64351 | 94 93 92 | 63447 | 63447 | 92 91 | 14400904 | 01 | 87992 | | 0 | 59 |
| | 10 | 29387 | 97 98 | 55960 | 91 | 52255 | 52255 | 92 91 | 03705 | | 85567 | 26 25 26 27 26 27 | 50 | |
| | 20 | 33585 | 97 98 | 47570 | 90 | 41064 | 41064 | 92 91 | 06506 | 02 | 83141 | 26 25 26 27 26 27 | 40 | |
| | 30 | 37783 | | 39181 | 8589 87 | 29873 | 29873 | | 09308 | 02 | 80716 | 26 25 26 27 26 27 | 30 | |
| | 40 | 41980 | 97 | 30792 | 8589 87 | 18682 | 18682 | 11189 87 | 12110 | | 78290 | 26 25 26 27 26 27 | 20 | |
| | 50 | 46178 | 98 | 22405 | 8589 87 | 07493 | 07493 | 11189 87 | 14912 | 03 | 75863 | 26 25 26 27 26 27 | 10 | |
| 2 | 0 | 50375 | 4197 | 14019 | | 54796304 | 54796304 | 11189 87 | 17715 | 03 | 73437 | 26 25 26 27 26 27 | 0 | 58 |
| | 10 | 54572 | | 05633 | | 85115 | 85115 | 11189 87 | 20518 | | 71010 | 26 25 26 27 26 27 | 50 | |
| | 20 | 58769 | | 69197249 | 84 | 73928 | 73928 | | 23321 | | 68583 | | 40 | |
| | 30 | 62966 | | 88866 | 83 | 62741 | 62741 | | 26125 | 04 | 66156 | | 30 | |
| | 40 | 67163 | 96 97 96 97 96 | 80483 | 82 81 80 79 78 77 76 | 51554 | 51554 | 86 | 28929 | | 63729 | | 20 | |
| | 50 | 71359 | 96 97 96 97 96 | 72101 | 82 81 80 79 78 77 76 | 40368 | 40368 | 86 | 31733 | 05 | 61302 | 28 | 10 | |
| 3 | 0 | 75556 | 96 97 96 97 96 | 63720 | 82 81 80 79 78 77 76 | 29182 | 29182 | 85 | 34538 | 05 | 58874 | 28 | 0 | 57 |
| | 30 | 79752 | 96 97 96 97 96 | 55340 | 82 81 80 79 78 77 76 | 17997 | 17997 | 84 | 37343 | | 56446 | | 50 | |
| | 20 | 83949 | 96 97 96 97 96 | 46961 | 82 81 80 79 78 77 76 | 06813 | 06813 | 83 | 40148 | | 54018 | | 40 | |
| | 30 | 88145 | 96 97 96 97 96 | 38583 | 82 81 80 79 78 77 76 | 54695630 | 54695630 | | 42953 | 06 | 51590 | | 30 | |
| | 40 | 92341 | | 30206 | 82 81 80 79 78 77 76 | 84447 | 84447 | 82 | 45759 | | 49162 | 29 | 20 | |
| | 50 | 96537 | | 21830 | 75 74 73 72 | 73265 | 73265 | | 48565 | 07 | 46733 | 29 | 10 | |
| 4 | 0 | 50100733 | 95 96 | 13455 | 75 74 73 72 | 62083 | 62083 | 81 80 | 51372 | | 44304 | | 0 | 56 |
| | 10 | 04928 | 95 96 | 05081 | 75 74 73 72 | 50902 | 50902 | 81 80 | 54179 | | 41875 | | 50 | |
| | 20 | 09124 | 95 96 | 69096708 | 75 74 73 72 | 39722 | 39722 | 81 80 | 56986 | 08 07 08 | 39446 | 30 | 40 | |
| | 30 | 13320 | 95 | 88336 | 75 74 73 72 | 28542 | 28542 | 79 | 59794 | 08 07 08 | 37016 | 29 | 30 | |
| | 40 | 17515 | 95 | 79964 | | 17363 | 17363 | 79 | 62601 | 08 07 08 | 34587 | 30 | 20 | |
| | 50 | 21710 | | 71593 | 71 69 | 06184 | 06184 | 77 78 77 | 65409 | 08 07 08 | 32157 | | 10 | |
| 5 | 0 | 25905 | | 63224 | 71 69 | 54595007 | 54595007 | 77 78 77 | 68217 | 09 | 29727 | 31 | 0 | 55 |
| | 10 | 30100 | | 34855 | 71 69 | 83829 | 83829 | 77 78 77 | 711026 | 69 | 27296 | 30 | 50 | |
| | 20 | 34295 | | 46487 | 68 | 72652 | 72652 | 76 75 | 73835 | 10 | 24866 | 31 | 40 | |
| | 30 | 38490 | | 38121 | 66 | 61476 | 61476 | 76 75 | 76645 | 09 | 22435 | 31 | 30 | |
| | 40 | 42685 | 94 95 | 29755 | 65 64 | 50301 | 50301 | 76 75 | 79454 | 10 | 20004 | | 20 | |
| | 50 | 46879 | 94 95 | 21390 | 65 64 | 39126 | 39126 | 74 | 82264 | | 17573 | | 10 | |
| | 60 | 51074 | 94 95 | 13026 | 65 64 | 27952 | 27952 | 74 | 85074 | | 15142 | | 0 | 54 |
| | | | | | | | Grad. 59. | Grad. 59. | Grad. 59. | Grad. 59. | Grad. 59. | Grad. 59. | S.M. | S.M. |
Libraries. Un. Ed.; Bodl. Oxf.; Brit. Mus. Lon.; Stadt. Breslau; Nat. Paris;
Johann Carl Schulze|wirklichen Mitgliedes der Königl. Preussischen Academie der|Wissenschaften| Neue Und Erweiterte| Sammlung | Logarithmischer, | Trigonometrischer | und anderer | Zum Gebrauch Der Mathematik | Unentbehrlicher | Tafeln. || II. Band. ||
Berlin, 1778. | Bey August Mylius, Buchhändler | In Der Brüderstrasse. |
Size 8 3/8 x 5 inches.
In this work the logarithms of the Magnus Canon of Ursinus are reprinted to every 10 seconds in the case of the first four and last four degrees, being the same as in the original. The logarithms from 4° to 86° are given for every minute only. Ursinus’ logarithms occupy half the lower portion of pp. 2–261 in Volume II., the title of the whole contents of these pages being:—
“Tafel | der | Sinus, Tangenten, | Secanten| und | deren sustimmenden briggischen und hyperboli-|schen Logarithmen | für die vier ersten und vier letzten Grade von 10 zu|10 Secunden;| für den übrigen Theil des Quadranten aber von Minute zu | Minute, nebet dem 6ten Theile der Differenzen | berechnet. |”
Joannis Kepleri|Imp. Cas. Ferdinandi II. | Mathematici | Chilias | Logarithmorum | Ad Totidem Numeros | Rotundos, | Przmissâ | Demonstratione Legitima | Ortus Logarithmorum eorumq. usus | Quibus | Nova Traditur Arithmetica, Seu | Compendium, quo post numerorum notitiam|nullum nec admirabilius, ​nec utilius solvendi pleraq. Problemata|Calculatoria, præsertim in Doctrina Triangulorum, citra| Multiplicationis, Divisionis Radicumq’. extractio-|nis, in Numeris prolixis, labores mole-|stissimos. | Ad | Illustriss. Principem & Dominum,| Dn. Philippvm | Landgravium Hassiæ, &c. | Cum Privilegio Authoris Cæsareo. |
Marpurgi,|Excusa Typis Casparis Chemlini.|cIɔ Iɔc xxiv.|
4°. Size 8 x 64 inches. A1$^1$, Title.A1$^2$, blank.Folding sheet with “***Ad Postul 2. Exemplum Sectionis⃜,”,A2$^1$, p. 3, Dedication by Kepler to Philip Landgrave of Hesse.A2$^2$–F3$^1$, pp. 4–45, “Demonstratio Struvctvræ Logarithmorvm.” in 30 propositions. F3$^2$–G4$^1$, pp. 46-55, “Methodvs Compendiosissima construendi Chiliada Logarithmorum.”
On G4$^2$ is the title “Chilias | Logarithmcrum | Joh, Kepleri, Mathem. | Casarei.|” H1$^1$–O$^2$, 52 pages occupied by the table, and at the foot of the last page “Errata,” 10 lines.
Signatures. A to N in fours + O in two = 54 leaves.
Paging. 55 numbered + 1 + 52 = 108 pages, also folding sheet.
Signature O is distinctly in two, the work ending with p. 108, but the Supplementum assumes it to end with p. 112, which it would have done had sig. O been in four.
Joannis Kepleri,| Imp. Cæs. Ferdinandi II.| Mathematici, | Supplementum | Chiliadis | Logarithmorum, | Continens | Præcepta De Eorum Usu,| Ad | IIlustriss. Principem et Dominum,|Dn. Philippum Land-|gravium Hassiæ, &c. |
Marpvrgi, | Ex officina Typographica Casparis Chemlini.| clɔ IɔcXXV. |
P1$^1$, p.[113], Title.P1$^2$, blank.P2$^1$–P3$^2$, pp. 113 [115]–116[118], 4 pages, “Joannis Kepleri Supplementum Chiliadis Logarithmorum, Continens Præcepta De Eorum Usu. Lectori S.”P4$^1$, p.[119] “Correctio Figurarum post punctum in Logarithmis.”P4$^2$, p.[120] “Preterea in textu Demonstrationum jam impresso, notaviista, nondum â Typographo animadversa.” 8 lines of corrections. Q1$^1$—Dd4$^2$, pp. 121-216. The work in 9 chapters. The pages are all headed “Joannis Kepleri Chiliadis Complement,” not Supplement.
Signatures. P to Z and Aa to Dd in fours = 52 leaves.
Paging. P. [113] to p. 216 = 104 pages.
Errors in Paging. Pages 115 to 118 containing the Preface are numbered in error 113 to 116.
The first part of the work contains Kepler’s demonstration of the structure of logarithms, which is in form geometrical, some of the ​
| Arcus Circuli cum differentiis. | Arcus Circuli cum differentiis. | Sinus feu Numeri abfoluti. | Partes vicefima quarta. | Logarithmi cum differentiis | Logarithmi cum differentiis | Partes fexage- naria. |
| | 3.55 | | | 206.40 | | |
| 29. 0.45 | 29. 0.45 | 48500.00 | 11. 38. 24 | 72360.64 | | 29. 6 |
| | 3. 56 | | | 205. 97 | | |
| 29. 4.41 | 29. 4.41 | 48600. 00 | 11. 39. 50 | 72154.67 | | 29. 10 |
| | 3. 56 | | | 205. 55 | | |
| 29. 8.37 | 29. 8.37 | 48700.00 | 11. 41.17 | 71949.12 | | 29. 13 |
| | 3. 56 | | | 205. 13 | | |
| 29. 12.33 | 29. 12.33 | 48800.00 | 11. 42. 43 | 71743.99 | | 29. 17 |
| | 3. 57 | | | 204. 71 | | |
| 29. 16. 30 | 29. 16. 30 | 48900.00 | 11. 44. 10 | 71539.28 | | 29. 20 |
| | 3. 56 | | | 204. 29 | | |
| 29. 20. 26 | 29. 20. 26 | 49000. 00 | 11. 45. 36 | 71334.99 | | 29. 24 |
| | 3. 57 | | | 203. 87 | | |
| 29. 24. 23 | 29. 24. 23 | 49100.00 | 11. 47. 2 | 71131.12 | − | 29. 28 |
| | 3. 57 | | | 203. 46 | | |
| 29. 28. 20 | 29. 28. 20 | 49200. 00 | 11. 48. 29 | 70927.66 | | 29. 31 |
| | 3. 57 | | | 203. 05 | | |
| 29. 32. 17 | 29. 32. 17 | 49300.00 | 11. 49. 55 | 70724.61 | + | 29. 35 |
| | 3. 58 | | | 202. 63 | | |
| 29. 36. 15 | 29. 36. 15 | 49400. 00 | 11. 51. 22 | 70521.98 | | 29. 38 |
| | 3. 57 | | | 202. 23 | | |
| 29. 40. 12 | 29. 40. 12 | 49500. 00 | 11. 52. 48 | 70319.75 | + | 29. 42 |
| | 3. 57 | | | 201. 81 | | |
| 29.44. 9 | 29.44. 9 | 49600.00 | 11. 54. 14 | 70117.94 | − | 29. 46 |
| | 3. 58 | | | 201. 41 | | |
| 29. 48. 7 | 29. 48. 7 | 49700. 00 | 11. 55.41 | 69916.53 | − | 29. 49 |
| | 3. 57 | | | 201. 01 | | |
| 29. 52. 4 | 29. 52. 4 | 49800.00 | 11. 57. 7 | 69715.52 | | 29. 53 |
| | 3. 58 | | | 200. 60 | | |
| 29. 56. 2 | 29. 56. 2 | 49900. 00 | 11. 58. 34 | 69514.92 | | 29. 56 |
| | 3. 58 | | | 200. 20 | | |
| 30. 0. 0 | 30. 0. 0 | 50000.00 | 12. 0. 0 | 69314.72 | | 30. 0 |
| | 3. 58 | | | 199. 80 | | |
| 30. 3. 58 | 30. 3. 58 | 50100.00 | 12. 1. 26 | 69114.92 | | 30. 4 |
| | 3. 59 | | | 199. 40 | | |
| 30. 7. 57 | 30. 7. 57 | 50200.00 | 12. 2. 53 | 68915.52 | − | 30. 7 |
| | 3. 58 | | | 199. 01 | | |
| 30. 11. 55 | 30. 11. 55 | 50300.00 | 12. 4. 19 | 68716.51 | + | 30. 11 |
| | 3. 59 | | | 198. 61 | | |
| 30. 15. 54 | 30. 15. 54 | 50400.00 | 12. 5.46 | 68517.90 | + | 30. 14 |
| | 3. 59 | | | 198. 21 | | |
| | | | | L 2 | Arcus | Arcus |
The logarithms in the Table are of the same kind as Napier’s, but they are not affected by the mistake in the computation of the Canon of 1614.
The Tables of Kepler and Napier are differently arranged, and the numbers for which the logarithms are given are also different. In Napier’s Canon the numbers in column “Sinus” are the values of sines of equidifferent arcs, while in this table the numbers or sines are equidifferent. For specimen page of the Table see preceding page. The arrangement is as follows:—
Column 2 contains 1000 equidifferent numbers, 10,000, 20,000, 30,000, … 9,980,000, 9,990,000, 10,000,000. It also has at the beginning the 36 numbers 1, 2, 3, to 9; 10, 20, 30 to 90}; 100, 200 to 900; and 1000, 2000 to 9000.
Column 4 contains the logarithms of the numbers in column 2, with interscript differences.
The 2nd and 4th are the only columns containing entries for the first 36 numbers.
It will be observed that a point marks off the last two figures of the values in these two columns, but if it be left out of account the numbers and logarithms agree with those of the Canon of 1614, in being referred to a radius of 10,000,000. So that the values really represented are the ratios of the numbers there given to 10,000,000.
Taking as an example the first entry in the specimen page, the number in column 2 which is 4,850,000 represents the ratio 4,850,000 to 10,000,000 or a 4840000/10000000th = a 485/1000th part of radius. Similarly column 1 gives the arc, in degrees, minutes, and seconds, corresponding to a sine equal to the 485/1000th part of the radius, with interscript differences;
Column 3 gives in hours, minutes, and seconds the 485/1000th part of a day of 24 hours; and finally
​Column 5 gives in minutes and seconds the 485/1000th part of a degree of 60 minutes.
Libraries. Sig. Ed.; Un. Gl.; Hunt. Mus. GI.; Bodl. Oxf.; Trin. Col. Dub.;
Tabvle Rudolphine. ... Ioannes Keplerus. ...
Ulmæ. Jonæ Saurii, Anno M.DC.XXVII.
Folio. Size 13 3/4 × 9 inches.
The logarithms used in this work are those of Napier.
Libraries. Adv. Edin.; etc.
Logarithmorvm | Cuilias Prima. |
Quam autor typis excudendam curauit, non eo con-| cilio, vt publici iuris fieret; sed partim, vt quorun-|dam suorum necessariorum desiderio priuatim satis- |faceret partim, vt eius adiumento, non solum Chilia-|das aliquot insequentes; sed etiam integrum Loga-|rithmorum Canonem, omnium Triangulorum cal-|culo inseruientem commodius absolueret. Habet e-|nim Canonem Sinuum, à seipso, ante Decennium, per| æquationes Algebraicas, & differentias, ipsis Sinu-|bus proportionales, prosingulis Gradibus & graduũ| centesimis, à primis fundamentis accurate extructũ:|quem vna cum Logarithmis adjvnctis, volente Deo, | in lucem sedaturum sperat, quam primum commode | licuerit. |
Quod autem hi Logarithmi, diversi sint ab ijs, | quos Clarissimus inuentor, memoriæ semper colendæ, | in suo edidit Canone Mirifico; sperandum, eius librũ | posthumum, abunde nobis propediem satisfactu-| rum. Qui autori (cum eum domi suæ, Edinburgi, | bis inuiseret, & apud eum humanissime exceptus, | per aliquot septimanas libentissime mansisset; eique | horum partem præcipuam quam tum absoluerat | ostendisset) suadere non ​destitit, vt hunc in|se laborem susciperet. Cui ille non|inuitus morem gessit. |
In tenui; sed non tenuis, structusve laborve.
8°, 16 pages.
The above short Preface occupies the first page of a small tract of sixteen pages, the remaining fifteen containing the natural numbers from 1 to 1000 with their logarithms, to base 10, to 14 places. The tract bears no author’s name or place or date of publication, but the evidence which assigns it to Briggs, and fixes the place and date of its publication as, London, 1617, seems conclusive. The Table of Logarithms is the first published to a base different from that employed by Napier.
It is unnecessary here to refer to subsequent works on Logarithms of a different kind from those originally published by Napier.
Libraries. Brit. Mus. Lon.;
Note.—In the foregoing Catalogue the only collections of Napier’s works referred to are in public libraries. The largest single collection, however, is that in possession of Lord Napier and Ettrick. Besides the editions more commonly met with, it embraces several not found in any of the public libraries of this country, as well as a copy of the rare ‘Ephemeris Motuum Celestium ad annum 1620,’ which contains Kepler’s letter of dedication to Napier, dated 27th July 1619.