The construction of the wonderful canon of logarithms

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78 Notes on Trigonometrical Propositions. rithms 581 261 and 312858, and the logarithm of the versed sine of the given angle —409615. The sum of these three logarithms is 484504, which is the logarithm of the difference between the versed sine of the base and the versed sine of the difference of the sides. Now the line corresponding to this logarithm, whether a versed sine or a common sine, is 6160057, and consequently this is the difference between the versed sine of the base and the versed sine of the difference of the sides. If to this you add the versed sine of the difference of the sides, that is 256300, the sum will be the versed sine of the base required, namely 6416357, and this subtracted from radius leaves the sine of the complement of the base, namely 3583643, which is the sine of 21°. Consequently the base required is 69°. Conversely, given three sides, to find any angle. Iffrom the logarithm of the difference between the versed sine of the base and the versed sine of the difference of the sides you subtract the logarithms of the sides, the remainder will be the logarithm of t/te versed sine of the angle soughtfor. As in the previous example, let the logarithms of the sides be 581 261 and 312858. Subtract their sum, 8941 19, from the logarithm 484504, and the remainder will be the negative logarithm— 409615, which gives the versed sine of the required angle 1 20° 24' 49". [c] Offive parts of a spherical triangle ] This proposition appears to be identical with the one which is inserted at the end, and distinguished like the former by (*). The latter proposition I consider much the superior. There are, however, three operations in it, the first two of which I throw into one, as they are better combined. Thus :— Let
Notes on Trigonometrical Propositions. 79 Let there be given the base 69°, the angles at the base -jo ?/ " 73° 36' 4" sum. 36° 48' 2" half sum. 53° 1 1' 58" complement of -^ sum. 1 1° 23' 54" difference. 5° 41' 57" half difference. 84° 18' 3" compl. of I diff. /"Sine half difference 5° 41' 57" Propor- J Sine half sum 36° 48' 2" tion i.\ Sine difference 11° 23' 54" \ Sum of sines Logarithms. 23095560 5124410 16213641 — 1757509
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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
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Introduction. xv in the way of syst
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Introduction. xvii on his mathemati
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Introduction. xix into English. The
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I TO THE READER STUDIOUS OF THE MAT
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To THE Reader. being left to the In
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1 8 Construction of the Canon. 2. O
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lo Construction of the Canon. less
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12 Construction of the Canon. easil
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14 Construction of the Canon. 9p co
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i6 Construction of the Canon. Third
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8 1 Construction of the Canon. 3 S,
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20 Construction of the Canon. 28. W
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2 2 Construction of the Canon. This
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— 24 Construction of the Canon. t
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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
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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 70 and 71: 46 Construction of the Canon. Outli
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 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
Page 121 and 122: Notes. 97 Different Methods describ
Page 123 and 124: — Notes. 99 io= looooooooo, the n
Page 125: A CATALOGU E OF THE WORKS OF JOHN N
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Page 130 and 131: — io6 Preliminary. Bibliographies
Page 133 and 134: downe cally the : A CATALOGUE OF TH
Page 135 and 136: ; The applying : Catalogue. i i i A
Page 137 and 138: 3| Catalogue. i 1 be explained in t
Page 139 and 140: Vande Catalogue. i i 5 2. Editions
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Page 143 and 144: ; Catalogue. 119 sitions and "Concl
Page 145 and 146: 1 Et | au 1 Catalogue. i 2 aussi la
Page 147 and 148: Harmonies En Par do. Catalogue. 123
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Page 151 and 152: 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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The construction of the wonderful canon of logarithms

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