The construction of the wonderful canon of logarithms

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46 Construction of the Canon. Outline of the Construction, in another form, of a Logarithmic Table. 60. OINCE the logarithms found by 54 sometimes differ ^ from those found 4y 58 {for example, the logarithm of the sine 378064 is 32752756 by the former, while by the latter it is 32752741), it would seem, that the table of sines is in some places faulty. Wherefore I advise the learned, who perchance may have plenty ofpupils and computers, to publish a table of sines m,ore reliable and with larger num,bers, in which radius is made 1 00000000, that is with eight cyphers after the unit instead of seven only. Then, let the First table, like ours, contain a hundred numbers progressing in the proportion of the new radius to the sine less than it by unity, namely of 1 00000000 to 99999999. Let the Second table also contain a hundred numbers in the proportion of this new radius to the number less than it by a hundred, namely of 100000000 to 99999900. Let the Third table, cilso called the Radical table, contain thirty-five columns with a hundred numbers in each column, and let the hundred numbers in each column progress in the proportion of ten thousand to the number less than it by unity, namely of 1 00000000 to 99990000. Let the thirty-five proportionals standing first in all the columns, or occupying the second, third, or other rank, progress among themselves in the proportion of 100 to 99, or of the new radius 1 00000000 to 99000000. In continuing these proportionals and finding their logarithms, let the other rules we have laid down be observed. From
Construction of the Canon, 47 FroM the Radical table completed in this way, you will find with great exactness (by 49 and 50) the logarithms of all sines between radius and the sine of 45 degrees ; from the arc of 45 degrees doubled, you will find (by 56) the logarithm, of half radius ; having obtained all these, you will find the other logarithms by 58. Arrange all these results as described in 59, andyou will produce a Table, certainly the most excellent of all Mathematical tables, andpreparedfor the most important uses. End of the Construction of the Logarithmic Table. F 4 Appendix.
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Cornell University Library The orig
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THE CONSTRUCTION OF THE WONDERFUL C
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To The Right Honourable FRANCIS BAR
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eJlCic^sdbsci^dlSjc^'b^ifesc:^ INTR
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Introduction. xiii Elizabeth on 24t
Page 19 and 20: Introduction. xv in the way of syst
Page 21 and 22: Introduction. xvii on his mathemati
Page 23: Introduction. xix into English. The
Page 27 and 28: I TO THE READER STUDIOUS OF THE MAT
Page 29: To THE Reader. being left to the In
Page 32 and 33: 1 8 Construction of the Canon. 2. O
Page 34 and 35: lo Construction of the Canon. less
Page 36 and 37: 12 Construction of the Canon. easil
Page 38 and 39: 14 Construction of the Canon. 9p co
Page 40 and 41: i6 Construction of the Canon. Third
Page 42 and 43: 8 1 Construction of the Canon. 3 S,
Page 44 and 45: 20 Construction of the Canon. 28. W
Page 46 and 47: 2 2 Construction of the Canon. This
Page 48 and 49: — 24 Construction of the Canon. t
Page 50 and 51: 26 Construction of the Canon. feren
Page 52 and 53: ; 28 Construction of the Canon. THU
Page 54 and 55: 30 Construction of the Canon. limit
Page 56 and 57: 32 Construction of the Canon. iiona
Page 58 and 59: 34 Construction of the Canon, the l
Page 60 and 61: 36 Construction of the Canon. table
Page 62 and 63: ; 38 Construction of the Canon. 51.
Page 64 and 65: 40 Construction of the Canon. find
Page 66 and 67: 42 Construction of the Canon. 45 de
Page 68 and 69: ; 44 Construction of the Canon. thr
Page 72 and 73: : Page 48 (^c^sS^^c3!ii(^'S^Sa:^J(:
Page 74 and 75: 50 Appendix. For as in statics, fro
Page 76 and 77: , A 52 Appendix. saving of half the
Page 78 and 79: 54 Appendix. But, you will say, the
Page 80 and 81: 56 Remarks on Appendix. Let the com
Page 82 and 83: 58 Remarks on Appendix. As the quot
Page 84 and 85: 6o Remarks on Appendix. but they ag
Page 86 and 87: 62 Remarks on Appendix. ber of qiio
Page 88 and 89: Page 64 SOME VERY REMARKABLE PROPOS
Page 90 and 91: — 66 Trigonometrical Propositions
Page 92 and 93: —; ; 68 Trigonometrical Propositi
Page 94 and 95: 70 Trigonometrical Propositions. Le
Page 96 and 97: 72 Trigonometrical Propositions. 14
Page 98 and 99: 74 Trigonometrical Propositions. Ag
Page 100 and 101: : Page 76 SOME NOTES BV THE LEARNED
Page 102 and 103: 78 Notes on Trigonometrical Proposi
Page 104 and 105: 8o Notes on Trigonometrical Proposi
Page 107 and 108: Notes BY THE TRANSLATOli L 2
Page 109 and 110: Notes. 85 On some Terms made use of
Page 111 and 112: Notes. 87 silence. For I await the
Page 113 and 114: — From RABDOLOGIM, Book I. Notes.
Page 115 and 116: ; Notes. 91 10,000,000 he multiplie
Page 117 and 118: Notes. 93 adapted to meet any requi
Page 119 and 120: Logarithms computed by Napier's Met
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Notes. 97 Different Methods describ
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— Notes. 99 io= looooooooo, the n
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A CATALOGU E OF THE WORKS OF JOHN N
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— I04 Preliminary. ment are added
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— io6 Preliminary. Bibliographies
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downe cally the : A CATALOGUE OF TH
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; The applying : Catalogue. i i i A
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3| Catalogue. i 1 be explained in t
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Vande Catalogue. i i 5 2. Editions
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dat Door Catalogue, i i 7 8°. Size
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; Catalogue. 119 sitions and "Concl
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1 Et | au 1 Catalogue. i 2 aussi la
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Harmonies En Par do. Catalogue. 123
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lohanne I Durch Liecht Darinen wund
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Catalogue. 127 Ausz begird der Warh
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Baron His At Catalogue. i 29 II.—
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— ; 1; Catalogue, i 3 1 1 1.—Ra
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& Arimmetica ; Catalogue. 133 This
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sender By van , Catalogue. 135 Reke
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Trigonometria I Logarithmorum — C
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; Logarithms, ; ; Catalogue. i 39 T
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;" Mirabilis Canonis expeditissimi
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Mirabilis Canonis ; Eiusque Catalog
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Printed English Invented With 1616.
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Baron ; Invented Catalogue. 147 Sig
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; ; Appendix. 149 The bloody Almana
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Desabvsement, des rinn Avec assigne
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Im I denburgischen nach Alsz meten
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; boutique ; mont Appendix. 155 des
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Colonic Canon Usibus | ; morum. ; S
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Appendix. 159 Grad. 30. + — MS. O
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Ex Logarithmorum, Multiplicationis,
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— ; Appendix, 163 man mathematici
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; Appendix. 165 titit, vt hunc in |
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Summary of Catalogue. 167 In German
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Summary of Appendix. 169 Traitd de
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