The construction of the wonderful canon of logarithms

More documents

Recommendations

Info

$'eries enti\`eres (+ [D78 Th d'Abel angulaire])$

; 38 Construction of the Canon. 51. All sines in theproportion of two to one have 6931 469. 2 2 for the difference of their logarithms. For since the ratio of every sine to its half is the same as that of radius to 5000000, therefore (by 36) the difference of the logarithms of any sine and of its half is the same as the difference of the logarithms of radius and of its half 5000000. But (by 34) the difference of the logarithms of radius and of the sine 5000000 is the same as the logarithm itself of the sine 5000000, and this logarithm (by 50) will be 6931469.22. Therefore, also, 6931469.22 will be the difference of all logarithms whose sines are in the proportion of two to one. Consequently the double of it, namely 13862938.44, will be the difference of all logarithms whose sines are in the ratio of four to one and the triple of it, namely 20794407.66, will be the difference of all logarithms whose sines are in the ratio of eight to one. 52. All sines in theproportion often to one have 23025842.34 for the difference of their logarithms. For (by 50) the sine 8000000 will have for its logarithm 2231434.68; and (by 51) the difference between the logarithms of the sine 8000000 and of its eighth part 1 000000, will be 20794407.66 ; whence by addition will be produced 23025842.34 for the logarithm of the sine 1 000000. And since radius is ten times this, all sines in the ratio of ten to one will have the same difference, 23025842.34, between their logarithms, for the reason and cause already stated (in 51) in reference to the proportion of two to one. And consequently the double of this logarithm, namely 46051684.68, will, as regards the difference of the logarithms, correspond to
Construction of the Canon. 39 to the proportion of a hundred to one ; and the triple of the same, namely 69077527.02, will be the difference of all logarithms whose sines are in the ratio of a thousand to one ; and so of the ratio ten thousand to one, and of the others as below. 53- Whence all sines in a ratio compounded of the ratios two to one and ten to one, have the difference of their logarithms formed from the differences 6931469.22 and 23025842.34 in the way shown in thefollowing
Page 2 and 3:
UbtafV
Page 4:
Cornell University Library The orig
Page 9 and 10:
THE CONSTRUCTION OF THE WONDERFUL C
Page 11: To The Right Honourable FRANCIS BAR
Page 15 and 16: eJlCic^sdbsci^dlSjc^'b^ifesc:^ INTR
Page 17 and 18: 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 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 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
Page 139 and 140:
Vande Catalogue. i i 5 2. Editions
Page 141 and 142:
dat Door Catalogue, i i 7 8°. Size
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
Page 149 and 150:
lohanne I Durch Liecht Darinen wund
Page 151 and 152:
Catalogue. 127 Ausz begird der Warh
Page 153 and 154:
Baron His At Catalogue. i 29 II.—
Page 155 and 156:
— ; 1; Catalogue, i 3 1 1 1.—Ra
Page 157 and 158:
& Arimmetica ; Catalogue. 133 This
Page 159 and 160:
sender By van , Catalogue. 135 Reke
Page 161 and 162:
Trigonometria I Logarithmorum — C
Page 163 and 164:
; Logarithms, ; ; Catalogue. i 39 T
Page 165 and 166:
;" Mirabilis Canonis expeditissimi
Page 167 and 168:
Mirabilis Canonis ; Eiusque Catalog
Page 169 and 170:
Printed English Invented With 1616.
Page 171 and 172:
Baron ; Invented Catalogue. 147 Sig
Page 173 and 174:
; ; Appendix. 149 The bloody Almana
Page 175 and 176:
Desabvsement, des rinn Avec assigne
Page 177 and 178:
Im I denburgischen nach Alsz meten
Page 179 and 180:
; boutique ; mont Appendix. 155 des
Page 181 and 182:
Colonic Canon Usibus | ; morum. ; S
Page 183 and 184:
Appendix. 159 Grad. 30. + — MS. O
Page 185 and 186:
Ex Logarithmorum, Multiplicationis,
Page 187 and 188:
— ; Appendix, 163 man mathematici
Page 189 and 190:
; Appendix. 165 titit, vt hunc in |
Page 191 and 192:
Summary of Catalogue. 167 In German
Page 193:
Summary of Appendix. 169 Traitd de
show all

The construction of the wonderful canon of logarithms

Create successful ePaper yourself

Delete template?

Save as template?