{"id":2212,"date":"2020-08-25T19:05:37","date_gmt":"2020-08-26T00:05:37","guid":{"rendered":"http:\/\/jonvoisey.net\/blog\/?p=2212"},"modified":"2020-08-25T19:05:37","modified_gmt":"2020-08-26T00:05:37","slug":"almagest-book-iv-table-of-lunar-equation-of-anomaly-first-anomaly","status":"publish","type":"post","link":"https:\/\/jonvoisey.net\/blog\/2020\/08\/almagest-book-iv-table-of-lunar-equation-of-anomaly-first-anomaly\/","title":{"rendered":"Almagest Book IV: Table of Lunar Equation of Anomaly (First Anomaly)"},"content":{"rendered":"

Although I don’t see any particular reason we couldn’t have done this several chapters earlier, Ptolemy has elected to hold off producing his table of Lunar Anomaly until almost the very end of Book IV<\/span>1<\/sup><\/a><\/span>.<\/p>\n

At the end of the previous chapter, he did toss in a few expository notes on this table noting that this will be useful in the future for “calculations concerning conjunctions and oppositions”<\/span>2<\/sup><\/a><\/span>. To do so, Ptolemy doesn’t show his math, but notes that it was done “geometrically, in the same way as we already did for the sun<\/a>.”<\/p>\n

However, to use that method requires knowing the ratio of the radius of the deferent to that of the epicycle. Ptolemy states he takes a ratio of $60:5 \\frac{1}{4}$. Using that, he calculates his table in the same manner as he did for the sun, which is in $6\u00ba$ intervals near apogee and $3\u00ba$ intervals near perigee. However, because this epicycle rotates opposite the direction of the deferent, we should subtract if the angle is in the first column, and add if it is in the second<\/span>3<\/sup><\/a><\/span><\/p>\n

That being laid out, the table is below:<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Angle from Apogee (<\/strong><\/span>\u00ba<\/strong>)<\/strong><\/span><\/td>\nEquation of Anomaly(\u00ba)<\/strong><\/span><\/td>\n<\/tr>\n
6<\/td>\n354<\/td>\n0;29<\/td>\n<\/tr>\n
12<\/td>\n348<\/td>\n0;57<\/td>\n<\/tr>\n
18<\/td>\n342<\/td>\n1;25<\/td>\n<\/tr>\n
24<\/td>\n336<\/td>\n1;53<\/td>\n<\/tr>\n
30<\/td>\n330<\/td>\n2;19<\/td>\n<\/tr>\n
36<\/td>\n324<\/td>\n2;44<\/td>\n<\/tr>\n
42<\/td>\n318<\/td>\n3;8<\/td>\n<\/tr>\n
48<\/td>\n312<\/td>\n3;31<\/td>\n<\/tr>\n
54<\/td>\n306<\/td>\n3;51<\/td>\n<\/tr>\n
60<\/td>\n300<\/td>\n4;8<\/td>\n<\/tr>\n
66<\/td>\n294<\/td>\n4;24<\/td>\n<\/tr>\n
72<\/td>\n288<\/td>\n4;38<\/td>\n<\/tr>\n
78<\/td>\n282<\/td>\n4;49<\/td>\n<\/tr>\n
84<\/td>\n276<\/td>\n4;56<\/td>\n<\/tr>\n
90<\/td>\n270<\/td>\n4;59<\/td>\n<\/tr>\n
93<\/td>\n267<\/td>\n5;0<\/td>\n<\/tr>\n
96<\/td>\n264<\/td>\n5;1<\/td>\n<\/tr>\n
99<\/td>\n261<\/td>\n5;0<\/td>\n<\/tr>\n
102<\/td>\n258<\/td>\n4;59<\/td>\n<\/tr>\n
105<\/td>\n255<\/td>\n4;57<\/td>\n<\/tr>\n
108<\/td>\n252<\/td>\n4;53<\/td>\n<\/tr>\n
111<\/td>\n249<\/td>\n4;49<\/td>\n<\/tr>\n
114<\/td>\n246<\/td>\n4;44<\/td>\n<\/tr>\n
117<\/td>\n243<\/td>\n4;38<\/td>\n<\/tr>\n
120<\/td>\n240<\/td>\n4;31<\/td>\n<\/tr>\n
123<\/td>\n237<\/td>\n4;24<\/td>\n<\/tr>\n
126<\/td>\n234<\/td>\n4;16<\/td>\n<\/tr>\n
129<\/td>\n231<\/td>\n4;7<\/td>\n<\/tr>\n
132<\/td>\n228<\/td>\n3;57<\/td>\n<\/tr>\n
135<\/td>\n225<\/td>\n3;46<\/td>\n<\/tr>\n
138<\/td>\n222<\/td>\n3;35<\/td>\n<\/tr>\n
141<\/td>\n219<\/td>\n3;23<\/td>\n<\/tr>\n
144<\/td>\n216<\/td>\n3;10<\/td>\n<\/tr>\n
147<\/td>\n213<\/td>\n2;57<\/td>\n<\/tr>\n
150<\/td>\n210<\/td>\n2;43<\/td>\n<\/tr>\n
153<\/td>\n207<\/td>\n2;28<\/td>\n<\/tr>\n
156<\/td>\n204<\/td>\n2;13<\/td>\n<\/tr>\n
159<\/td>\n201<\/td>\n1;57<\/td>\n<\/tr>\n
162<\/td>\n198<\/td>\n1;41<\/td>\n<\/tr>\n
165<\/td>\n195<\/td>\n1;25<\/td>\n<\/tr>\n
168<\/td>\n192<\/td>\n1;9<\/td>\n<\/tr>\n
171<\/td>\n189<\/td>\n0;52<\/td>\n<\/tr>\n
174<\/td>\n186<\/td>\n0;35<\/td>\n<\/tr>\n
177<\/td>\n183<\/td>\n0;18<\/td>\n<\/tr>\n
180<\/td>\n180<\/td>\n0;0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

\"\"<\/a><\/p>\n

\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Although I don’t see any particular reason we couldn’t have done this several chapters earlier, Ptolemy has elected to hold off producing his table of Lunar Anomaly until almost the very end of Book IV. At the end of the previous chapter, he did toss in a few expository notes on this table noting that … <\/p>\n

Continue reading “Almagest Book IV: Table of Lunar Equation of Anomaly (First Anomaly)”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[24],"tags":[25,19,14],"class_list":["post-2212","post","type-post","status-publish","format-standard","hentry","category-almagest","tag-almagest","tag-moon","tag-ptolemy"],"acf":[],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p9ZpvC-zG","_links":{"self":[{"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/posts\/2212","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/comments?post=2212"}],"version-history":[{"count":1,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/posts\/2212\/revisions"}],"predecessor-version":[{"id":2214,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/posts\/2212\/revisions\/2214"}],"wp:attachment":[{"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/media?parent=2212"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/categories?post=2212"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/tags?post=2212"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}