cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.17171/1-2-280-1
title: Diagram MAPD0280

description: Solar Epicycle: An epicycle is a circle whose center is fixed on and revolves around the periphery of another circle at a uniform speed. The epicycle itself will rotate at its own uniform speed. Manuscript diagrams for this topic are recognizably related to each other, but the details of the epicyclic circles vary and suggest some difficulty in the understanding by early medieval scholars of these combinations of circular motions. Calcidius states that the motions of the circles are uniform, although his description omits some potentially useful elements, such as the division of the epicycle into four equal quadrants; he does this explicitly only for the deferent circle. His definition of an epicycle is extremely general. The geometrical framework is simple. The same zodiacal circle ABΓΔ, ordered anti-clockwise, as used in the explanation by an eccentric circle appears again here. The earth is at the center Θ. Concentric with the zodiacal circle is the deferent circle MONΞ (anti-clockwise). The epicyclic circle has its center initially at M. The periphery of the epicycle is labelled anti-clockwise EZHK. The rotation of each of these three circles is specified. ABΓΔ rotates daily in a clockwise direction. MONΞ rotates with the planetary orbital speed --- once a year in the case of the Sun --- anti-clockwise. The epicycle EZHK rotates at a speed specific to the planet, in this case, for the Sun, once a year clockwise.With the motion of the epicycle's center on the deferent from M to O, the epicyclic circle is oriented so that E remains outermost and towards the zodiacal point B. The Sun, located on the epicycle initially at E, rotates 90° to the point K, which is the uppermost point on the epicycle when its center is at O. This combination of motions continues from quadrant to quadrant through the year, at the end of which the solar epicycle will return to M and the Sun on the periphery of the epicycle will return to point E. But as the annual motion of the Sun occurs, the appearance from the earth, at the center of the deferent and zodiacal circles, is that the Sun moves faster from K to H and H to Z than it moves from E to K and Z to E. This appearance of varying speed can be understood by noticing that from E to K and from Z to E the Sun seems to move slower than the center of the solar epicycle from M to O and from Ξ to M; conversely from K to H and from H to Z the Sun seems to move faster than the center of the epicycle from nO to N and from N to Ξ. And the Sun at H is closest to the earth and at E is farthest from the earth during the annual motion. All this is as seen from the earth, and the motions of the circles remain uniform.
description: Medieval Diagrams
DOI: 10.17171/1-2-282-1
title: Diagram MAPD0282

description: Bounded Elongation of Venus Desciptive: The manuscript diagrams for this text and for that following it, the epicyclic explanation of Venus's elongation, are among the most corrupted in all of the Calcidian corpus. The positions of X and K vary extensively, and there are usually two concentric circles within the zodiacal circle, neither of which is called for by the text. However, most scribes either chose not to correct these variants in their exemplars or else did not recognize any error in such variant diagrams. From the eleventh century onward, some scholars did recognize and correct them. The text calls for a severely descriptive, not explanatory, image. The zodiacal circle, a central earth at X, a radius passing through the Sun's center K to the point B, and two radii to two zodiacal points A and Γ, located respectively 50° to the east and to the west of B, are sufficient to complete the diagram. With the Sun always seen along XKB, the planet Venus never appears farther away from it than the two limiting radii XA and XΓ at angles of 50° from XKB.
description: Medieval Diagrams
DOI: 10.17171/1-2-283-1
title: Diagram MAPD0283

description: Length of Seasons: The description in the text and the diagrams in the manuscripts coincide well. The purpose of the diagram is solely to show that the four equal quadrants of the zodiac contain four unequal lengths of the year and what those lengths are. Initially the circle of the twelve signs is laid out, usually within a circular band, sometimes on the outside of a single circle. The four cardinal points ABΓΔ are set anti-clockwise at 90-degree intervals, beginning with A at Aries 0° and at 12 o'clock. Two perpendicular diameters connect the pairs of points AΓ and BΔ. The letter Θ appears at the centerpoint, where the diameters intersect.
description: Medieval Diagrams
DOI: 10.17171/1-2-286-1
title: Diagram MAPD0286

description: Solar Epicycle: An epicycle is a circle whose center is fixed on and revolves around the periphery of another circle at a uniform speed. The epicycle itself will rotate at its own uniform speed. Manuscript diagrams for this topic are recognizably related to each other, but the details of the epicyclic circles vary and suggest some difficulty in the understanding by early medieval scholars of these combinations of circular motions. Calcidius states that the motions of the circles are uniform, although his description omits some potentially useful elements, such as the division of the epicycle into four equal quadrants; he does this explicitly only for the deferent circle. His definition of an epicycle is extremely general. The geometrical framework is simple. The same zodiacal circle ABΓΔ, ordered anti-clockwise, as used in the explanation by an eccentric circle appears again here. The earth is at the center Θ. Concentric with the zodiacal circle is the deferent circle MONΞ (anti-clockwise). The epicyclic circle has its center initially at M. The periphery of the epicycle is labelled anti-clockwise EZHK. The rotation of each of these three circles is specified. ABΓΔ rotates daily in a clockwise direction. MONΞ rotates with the planetary orbital speed --- once a year in the case of the Sun --- anti-clockwise. The epicycle EZHK rotates at a speed specific to the planet, in this case, for the Sun, once a year clockwise.With the motion of the epicycle's center on the deferent from M to O, the epicyclic circle is oriented so that E remains outermost and towards the zodiacal point B. The Sun, located on the epicycle initially at E, rotates 90° to the point K, which is the uppermost point on the epicycle when its center is at O. This combination of motions continues from quadrant to quadrant through the year, at the end of which the solar epicycle will return to M and the Sun on the periphery of the epicycle will return to point E. But as the annual motion of the Sun occurs, the appearance from the earth, at the center of the deferent and zodiacal circles, is that the Sun moves faster from K to H and H to Z than it moves from E to K and Z to E. This appearance of varying speed can be understood by noticing that from E to K and from Z to E the Sun seems to move slower than the center of the solar epicycle from M to O and from Ξ to M; conversely from K to H and from H to Z the Sun seems to move faster than the center of the epicycle from nO to N and from N to Ξ. And the Sun at H is closest to the earth and at E is farthest from the earth during the annual motion. All this is as seen from the earth, and the motions of the circles remain uniform.
description: Medieval Diagrams
DOI: 10.17171/1-2-287-1
title: Diagram MAPD0287

description: Generic Epicycle: The manuscript diagrams for the generic epicycle follow generally the description of Calcidius's text. The most common divergence from the text's description is a failure of the radii tangent to the epicycle to be, in fact, tangent. Calcidius's account here might not be clear to a reader not already familiar with such a diagram. The purpose of the diagram is to identify the forward and retrograde arcs of the epicycle as well as the stationary points of the planet on the epicycle. The zodiacal circle and the earth at its center are specified first. The epicyclic circle EZH is then presented, but the text requires a preexisting diagram and simply discusses the motion of points on the diagram. The three points labeling the epicycle only become clear as the description proceeds, the points Z and H being the points of tangency with the two radii drawn to the zodiacal circle and the point E being between the zodiacal point A and the center M of the epicycle along a radius from the earth through M to A. Once this figure is recognized, the reader can follow Calcidius's account of epicyclic motion, which he applies here to any planet and gives no specifics of planetary motion. The epicycle here is fixed and does not move around the zodiac. The epicycle only rotates, with its motion in the same sense as the celestial sphere, from east to west, showing the motion of a planet on its periphery. Calcidius point out the two locations, or regions, of planetary station in two very small arcs including the tangent points H and Z. He then labels the passage from Z through E to H as the proper motion of the planet on the periphery of the epicycle and the passage from H to Z as the retrograde motion of the planet. He continually reminds the reader that the planetary motions are seen against the background of the zodiac rather than directly on the epicyclic circle.
description: Medieval Diagrams
DOI: 10.17171/1-2-288-1
title: Diagram MAPD0288

description: Bounded Elongation of Venus Epicyclic: The manuscript diagrams for this text are often confusing, and it is less easy to categorize them than the diagrams for the previous text, which gives the observational account of Venus's elongation. As the text says, the epicyclic explanation builds upon the immediately preceding text that describes the visible elongation. However, with the positions of X and K already misplaced in most of the diagrams for the prior text, any attempt to add an epicyclic circle for Venus would usually result in further error. Nonetheless, certain scholars of the eleventh century did reconstruct the diagrams correctly from the text. The epicyclical account of Venus's elongation prescribes a circle cutting the zodiacal radius XKB. This radius passes from the earth through the Sun at K, but the distance from X to K is nowhere stated. While it would seem proper to make this radius bisect the epicyclic circle, the location of K is possible at the center of the epicycle, below this center, or completely outside and below the epicycle. The last option would fit Plato's planetary order, which has Venus farther than the Sun from the earth. In any case, Calcidius does not specify the location of K with respect to the epicycle. The main purpose of the epicycle is not to show the order of planets but to show the limited movement of Venus with respect to the Sun, and the account does this. The epicycle ΔEZH is drawn into the preexisting diagram for the simple phenomenal description so that the epicycle fits between the zodiacal circle ABΓ and its center X and is tangent to the two preset radii XA and XΓ, which pass to points 50° to either side of the zodiacal point B.
description: Medieval Diagrams
DOI: 10.17171/1-2-291-1
title: Diagram MAPD0291

description: Absque Libra: The diagram simply uses a vertical line to demarcate the beginning of the sign of Libra and then shows the Sun at mid-latitude before entering the sign while showing the Sun one half a degree above and below its previous latitude after entering Libra. Four horizontal parallels, equally spaced, are cut by a vertical line. To the left of the vertical there appears a small circle in the middle space formed by the four parallels. To the right of the vertical there appear two small circles, one bisected by the second parallel down, the other bisected by the third parallel down. These two circles to the right of the vertical are placed with the upper circle distinctly to the left of the lower circle. On the right side of the vertical line there appears above the four parallels the letter "L". Below the top parallel, to the right of the vertical line, is the phrase from the text, "absque Libre confinio", or some variant of this.
description: Medieval Diagrams
DOI: 10.17171/1-2-294-1
title: Diagram MAPD0294

description: Libra Aries: We find three feasible interpretations for this diagram. One interpretation emphasizes the mention by Capella (VIII.872) of successive diametrically opposed points along the ecliptic as the sun makes its daily motion. In this passage Capella names first the opposing signs of Aries and Libra as he describes the daily passage. A second interpretation emphasizes the four numbered sections and the opposing signs as elements of Capella's description (VIII.874) of the emergence of opposite seasons on opposite sides of the globe, with the numbers referring to the four seasons and the signs Libra and Aries as the signs for equinoxes and the change of seasons. A third interpretation has elements of both the preceding ones but refers more closely to the second (VIII.874). The signs Libra and Aries are the signs for equinoctial changes of seasons, and the four numerals refer to the first four degrees of these two signs, where, according to recognized authority (Bede, De temporum ratione, 6) the equinoxes occurred at the time of Creation, at 4° of Aries and at 4° of Libra. Johannes Scottus (Eriugena), "Annotationes in Marcianum", ed. C. Lutz (Cambridge: Mediaeval Academy of America, 1939), p. 168(at 427,6) used this definition of the equinoxes. Eriugena wrote this in the 850s. An outer circle contains a small central circle and ten lines connecting the outer with the inner circle. These ten lines are in some cases separate lines and in other cases segments of radial lines. The ten lines appear in two groups that oppose each other. Commonly the four spaces constituted by a group of five lines contain the numerals from one to four; these numerals are always arranged as opposites. That is, proceeding counter-clockwise, we find the first space in each group with the numeral for one, and so forth. Outside this arrangement of two circles with connecting lines are written the names, or abbreviations, of the two signs Libra and Aries. Each of the names appears close to one of the groups of five lines.
description: Medieval Diagrams
DOI: 10.17171/1-2-306-1
title: Diagram MAPD0306

description: Partes Angustantur: The diagram represents the cosmological and geometrical fact that an object or an arc of a given metrical length will fill a smaller and smaller angle as it is removed from the center. In the text created for this diagram the emphasis is upon the narrowing of angular arcs, and thus of planetary orbits, to shorter and shorter lengths as one approaches the central earth. This diagram can also function as an optical diagram to show that two arcs of equal length traced by two radii of different lengths will appear under different visual angles. I is worth noting that this reasoning also appears near the end of the Plinian excerpt (see above) "De Absidibus earum": nearer planets move faster, and motion at apogee is slowest. Two concentric circles are connected by a number of radial line segments, usually sixteen or more (not twelve). The only elaboration in the diagram is the label written circularly within the outer circle. In all but one case this label is "partes angustantur iuxta terram".
description: Medieval Diagrams
DOI: 10.17171/1-2-225-1
title: Diagram MAPD0225

description: Generic Epicycle: The manuscript diagrams for the generic epicycle follow generally the description of Calcidius's text. The most common divergence from the text's description is a failure of the radii tangent to the epicycle to be, in fact, tangent. Calcidius's account here might not be clear to a reader not already familiar with such a diagram. The purpose of the diagram is to identify the forward and retrograde arcs of the epicycle as well as the stationary points of the planet on the epicycle. The zodiacal circle and the earth at its center are specified first. The epicyclic circle EZH is then presented, but the text requires a preexisting diagram and simply discusses the motion of points on the diagram. The three points labeling the epicycle only become clear as the description proceeds, the points Z and H being the points of tangency with the two radii drawn to the zodiacal circle and the point E being between the zodiacal point A and the center M of the epicycle along a radius from the earth through M to A. Once this figure is recognized, the reader can follow Calcidius's account of epicyclic motion, which he applies here to any planet and gives no specifics of planetary motion. The epicycle here is fixed and does not move around the zodiac. The epicycle only rotates, with its motion in the same sense as the celestial sphere, from east to west, showing the motion of a planet on its periphery. Calcidius point out the two locations, or regions, of planetary station in two very small arcs including the tangent points H and Z. He then labels the passage from Z through E to H as the proper motion of the planet on the periphery of the epicycle and the passage from H to Z as the retrograde motion of the planet. He continually reminds the reader that the planetary motions are seen against the background of the zodiac rather than directly on the epicyclic circle.
description: Medieval Diagrams
DOI: 10.17171/1-2-227-1
title: Diagram MAPD0227

description: Bounded Elongation of Venus Epicyclic: The manuscript diagrams for this text are often confusing, and it is less easy to categorize them than the diagrams for the previous text, which gives the observational account of Venus's elongation. As the text says, the epicyclic explanation builds upon the immediately preceding text that describes the visible elongation. However, with the positions of X and K already misplaced in most of the diagrams for the prior text, any attempt to add an epicyclic circle for Venus would usually result in further error. Nonetheless, certain scholars of the eleventh century did reconstruct the diagrams correctly from the text. The epicyclical account of Venus's elongation prescribes a circle cutting the zodiacal radius XKB. This radius passes from the earth through the Sun at K, but the distance from X to K is nowhere stated. While it would seem proper to make this radius bisect the epicyclic circle, the location of K is possible at the center of the epicycle, below this center, or completely outside and below the epicycle. The last option would fit Plato's planetary order, which has Venus farther than the Sun from the earth. In any case, Calcidius does not specify the location of K with respect to the epicycle. The main purpose of the epicycle is not to show the order of planets but to show the limited movement of Venus with respect to the Sun, and the account does this. The epicycle ΔEZH is drawn into the preexisting diagram for the simple phenomenal description so that the epicycle fits between the zodiacal circle ABΓ and its center X and is tangent to the two preset radii XA and XΓ, which pass to points 50° to either side of the zodiacal point B.
description: Medieval Diagrams
DOI: 10.17171/1-2-229-1
title: Diagram MAPD0229

description: Length of Seasons: The description in the text and the diagrams in the manuscripts coincide well. The purpose of the diagram is solely to show that the four equal quadrants of the zodiac contain four unequal lengths of the year and what those lengths are. Initially the circle of the twelve signs is laid out, usually within a circular band, sometimes on the outside of a single circle. The four cardinal points ABΓΔ are set anti-clockwise at 90-degree intervals, beginning with A at Aries 0° and at 12 o'clock. Two perpendicular diameters connect the pairs of points AΓ and BΔ. The letter Θ appears at the centerpoint, where the diameters intersect.
description: Medieval Diagrams
DOI: 10.17171/1-2-231-1
title: Diagram MAPD0231

description: Solar Epicycle: An epicycle is a circle whose center is fixed on and revolves around the periphery of another circle at a uniform speed. The epicycle itself will rotate at its own uniform speed. Manuscript diagrams for this topic are recognizably related to each other, but the details of the epicyclic circles vary and suggest some difficulty in the understanding by early medieval scholars of these combinations of circular motions. Calcidius states that the motions of the circles are uniform, although his description omits some potentially useful elements, such as the division of the epicycle into four equal quadrants; he does this explicitly only for the deferent circle. His definition of an epicycle is extremely general. The geometrical framework is simple. The same zodiacal circle ABΓΔ, ordered anti-clockwise, as used in the explanation by an eccentric circle appears again here. The earth is at the center Θ. Concentric with the zodiacal circle is the deferent circle MONΞ (anti-clockwise). The epicyclic circle has its center initially at M. The periphery of the epicycle is labelled anti-clockwise EZHK. The rotation of each of these three circles is specified. ABΓΔ rotates daily in a clockwise direction. MONΞ rotates with the planetary orbital speed --- once a year in the case of the Sun --- anti-clockwise. The epicycle EZHK rotates at a speed specific to the planet, in this case, for the Sun, once a year clockwise.With the motion of the epicycle's center on the deferent from M to O, the epicyclic circle is oriented so that E remains outermost and towards the zodiacal point B. The Sun, located on the epicycle initially at E, rotates 90° to the point K, which is the uppermost point on the epicycle when its center is at O. This combination of motions continues from quadrant to quadrant through the year, at the end of which the solar epicycle will return to M and the Sun on the periphery of the epicycle will return to point E. But as the annual motion of the Sun occurs, the appearance from the earth, at the center of the deferent and zodiacal circles, is that the Sun moves faster from K to H and H to Z than it moves from E to K and Z to E. This appearance of varying speed can be understood by noticing that from E to K and from Z to E the Sun seems to move slower than the center of the solar epicycle from M to O and from Ξ to M; conversely from K to H and from H to Z the Sun seems to move faster than the center of the epicycle from nO to N and from N to Ξ. And the Sun at H is closest to the earth and at E is farthest from the earth during the annual motion. All this is as seen from the earth, and the motions of the circles remain uniform.
description: Medieval Diagrams