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The chord function and the table: add link https://en.m.wikipedia.org/wiki/Minute_and_second_of_arc
[td]: <math> \frac{\operatorname{chord} \left(\theta + \tfrac12^\circ \right) - \operatorname{chord} \left( \theta^\circ\right)}{30}. </math>[/td] [td][/td]
[td][/td] [td]This is the average number of sixtieths of a unit that must be added to chord(''ΞΈ''Β°) each time the angle increases by one minute of arc, between the entry for ''ΞΈ''Β° and that for (''ΞΈ'' + {{sfrac|1|2}})Β°. Thus, it is used for [[linear interpolation]]. Glowatzki and GΓΆttsche showed that Ptolemy must have calculated chords to five sexigesimal places in order to achieve the degree of accuracy found in the "sixtieths" column.<ref name=Toomer>[https://classicalliberalarts.com/resources/PTOLEMY_ALMAGEST_ENGLISH.pdf# Toomer's translation of the Almaagest],1984, footnote 68, pages 57-59.</ref><ref>Ernst Glowatzki and Helmut GΓΆttsche, ''Die Sehnentafel des Klaudios Ptolemaios. Nach den historischen FormelplΓ€nen neuberechnet.'', MΓΌnchen, 1976.</ref>[/td]
[td]This is the average number of sixtieths of a unit that must be added to chord(''ΞΈ''Β°) each time the angle increases by one [[Minute_and_second_of_arc|minute of arc]], between the entry for ''ΞΈ''Β° and that for (''ΞΈ'' + {{sfrac|1|2}})Β°. Thus, it is used for [[linear interpolation]]. Glowatzki and GΓΆttsche showed that Ptolemy must have calculated chords to five sexigesimal places in order to achieve the degree of accuracy found in the "sixtieths" column.<ref name=Toomer>[https://classicalliberalarts.com/resources/PTOLEMY_ALMAGEST_ENGLISH.pdf# Toomer's translation of the Almaagest],1984, footnote 68, pages 57-59.</ref><ref>Ernst Glowatzki and Helmut GΓΆttsche, ''Die Sehnentafel des Klaudios Ptolemaios. Nach den historischen FormelplΓ€nen neuberechnet.'', MΓΌnchen, 1976.</ref>[/td] [td][/td]
[td][/td] [td]: <math>[/td]
[td]: <math>[/td]
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[td]: <math> \frac{\operatorname{chord} \left(\theta + \tfrac12^\circ \right) - \operatorname{chord} \left( \theta^\circ\right)}{30}. </math>[/td]Revision as of 19:03, 30 August 2025
[/td][td]: <math> \frac{\operatorname{chord} \left(\theta + \tfrac12^\circ \right) - \operatorname{chord} \left( \theta^\circ\right)}{30}. </math>[/td] [td][/td]
[td][/td] [td]This is the average number of sixtieths of a unit that must be added to chord(''ΞΈ''Β°) each time the angle increases by one minute of arc, between the entry for ''ΞΈ''Β° and that for (''ΞΈ'' + {{sfrac|1|2}})Β°. Thus, it is used for [[linear interpolation]]. Glowatzki and GΓΆttsche showed that Ptolemy must have calculated chords to five sexigesimal places in order to achieve the degree of accuracy found in the "sixtieths" column.<ref name=Toomer>[https://classicalliberalarts.com/resources/PTOLEMY_ALMAGEST_ENGLISH.pdf# Toomer's translation of the Almaagest],1984, footnote 68, pages 57-59.</ref><ref>Ernst Glowatzki and Helmut GΓΆttsche, ''Die Sehnentafel des Klaudios Ptolemaios. Nach den historischen FormelplΓ€nen neuberechnet.'', MΓΌnchen, 1976.</ref>[/td]
[td]This is the average number of sixtieths of a unit that must be added to chord(''ΞΈ''Β°) each time the angle increases by one [[Minute_and_second_of_arc|minute of arc]], between the entry for ''ΞΈ''Β° and that for (''ΞΈ'' + {{sfrac|1|2}})Β°. Thus, it is used for [[linear interpolation]]. Glowatzki and GΓΆttsche showed that Ptolemy must have calculated chords to five sexigesimal places in order to achieve the degree of accuracy found in the "sixtieths" column.<ref name=Toomer>[https://classicalliberalarts.com/resources/PTOLEMY_ALMAGEST_ENGLISH.pdf# Toomer's translation of the Almaagest],1984, footnote 68, pages 57-59.</ref><ref>Ernst Glowatzki and Helmut GΓΆttsche, ''Die Sehnentafel des Klaudios Ptolemaios. Nach den historischen FormelplΓ€nen neuberechnet.'', MΓΌnchen, 1976.</ref>[/td] [td][/td]
[td][/td] [td]: <math>[/td]
[td]: <math>[/td]
Continue reading...
