{"id":3289,"date":"2022-05-07T15:32:31","date_gmt":"2022-05-07T20:32:31","guid":{"rendered":"https:\/\/jonvoisey.net\/blog\/?p=3289"},"modified":"2022-05-07T15:32:31","modified_gmt":"2022-05-07T20:32:31","slug":"almagest-book-vi-table-of-angles-of-inclination-at-eclipses","status":"publish","type":"post","link":"https:\/\/jonvoisey.net\/blog\/2022\/05\/almagest-book-vi-table-of-angles-of-inclination-at-eclipses\/","title":{"rendered":"Almagest Book VI: Table of Angles of Inclination at Eclipses"},"content":{"rendered":"

As usual, after completing a few example calculations, Ptolemy lays out the table discussed in the last post. I’ve again made this table available as a Google Sheet<\/a>.<\/p>\n

\"\"<\/a>We can briefly follow Ptolemy’s description of this table in which<\/p>\n

we computed the sizes of the angles for the other [integer] digits [of magnitude], [always taking] that angle which was less than a right angle, in units where one right angle equals $90\u00ba$ (corresponding to the graduation of the quadrant of the horizon). We constructed a table with $22$ lines and $4$ columns. The first column contains the digits of actual obscuration, measured along the diameter, found for mid-eclipse; the second contains the angles occurring at solar eclipses at the moment of the beginning of the eclipse and the moment of the end of emersion; the third contains the angles occurring at lunar eclipses at the moment of the beginning of the eclipse and of the end of emersion; and the fourth contains the angles occurring at lunar eclipses at the moment of the end [of the partial phase of] the eclipse and the moment of the beginning of emersion.<\/p><\/blockquote>\n

The table is quite straightforward and we can see that values we calculated in the last post.<\/p>\n

What might not be immediately obvious is why columns $2$ and $4$ are incomplete. This is because for solar eclipses (in column $2$, they can never be “more than complete” since the sizes of the lunar and solar discs are so close. Thus, an obscuration of $12$ digits is the maximum. For the moon, they can be, so Ptolemy calculates these in column $3$. In column $4$, this is specifically for the first and last moments of totality, so anything less than $12$ digits doesn’t make any sense.<\/p>\n

As a quick note, the circular table we explored in the last post was actually part of this chapter as well, but is made more sense to display it there.<\/p>\n

\n

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

\n

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

As usual, after completing a few example calculations, Ptolemy lays out the table discussed in the last post. I’ve again made this table available as a Google Sheet.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","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":[25,46,14],"class_list":["post-3289","post","type-post","status-publish","format-standard","hentry","category-almagest","tag-almagest","tag-eclipse","tag-ptolemy"],"acf":[],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p9ZpvC-R3","_links":{"self":[{"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/posts\/3289","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=3289"}],"version-history":[{"count":1,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/posts\/3289\/revisions"}],"predecessor-version":[{"id":3292,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/posts\/3289\/revisions\/3292"}],"wp:attachment":[{"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/media?parent=3289"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/categories?post=3289"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/tags?post=3289"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}