The construction of the wonderful canon of logarithms

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Page 64 SOME VERY REMARKABLE PROPOSITIONS FOR THE solution of spherical triangles with wonderfod ease. To solve a spherical triangle without dividing it into two quadrantal or rectangular triangles. IvEN three sides, to find any angle. And conversely, Given three angles, to find any side. This is best done by the three methods explained in my work on Logarithms, Book II. chap, VI sects. 8, 9, 10. Given the side h.T>, & the angles T) & ^, to find the side A B. Multiply the sine of A D by the sine of D ; divide the product by the sine of B, and you will have the sine of A B. 4. Given
; Trigonometrical Propositions. 65 4. Given the side h. T>, & the angles T> & V>, to find the side B D. D ; Multiply radius by the sine of the complement of divide by the tangent of the complement of A D, and you will obtain the tangent of the arc C D : then multiply the sine of C D by the tangent of D ; divide the product by the tangent of B, and the sine of B C will result : C D, and you have B D. add or subtract B C and 5. Given the side A D, df the angles D cSf B, /c find the angle A. Multiply radius by the sine of the complement of divide by the tangent of' the complement of A D ; D, and the tangent of the complement of C A D will be produced ; whence we have CAD itself. Similarly multiply the sine of the complement of B by the sine of C A D ; divide by the sine of the complement of D, and the sine of B A C will be produced ; which being added to or subtracted from CAD, you will obtain the required angle BAD. 6. Given KTi, & the angle D with the side B D, to find the angle B. Multiply radius by the sine of the complement of divide by the tangent of the complement of D ; A D, and the tangent of C D will be produced ; arc C D subtract from, or add to, the side B D, and you have B C : then multiply the sine of C D by the tangent of D ; divide the product by the sine of B C, and you have the tangent of the angle B. 7. Given A D, cSj' the angle D with the side B D, to find the side A B. Multiply radius by the sine of the complement of D ; divide the product by the tangent of the com- be I produced plement of A D, and the tangent of C D will its
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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
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 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 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
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
Page 128 and 129: — I04 Preliminary. ment are added
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
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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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