... ja

The single-character alternate version code "a'' on the various FITS keywords was introduced in Paper I. It has values blank and A through Z.

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... celestial

Usage here of the conventional symbols for right ascension and declination for celestial coordinates is meant only as a mnemonic. It does not preclude other celestial systems.

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... axes

We will refer to these simply as "the CRVAL ia'', and likewise for the other keyword values.

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... galactic

"New'' galactic coordinates are assumed here, Blaauw et al. (1960). Users of the older system or future systems should adopt a different value of x and document its meaning.

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... helioecliptic

Ecliptic and helioecliptic systems each have their equator on the ecliptic. However, the reference point for ecliptic longitude is the vernal equinox while that for helioecliptic longitude is the sun vector.

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... keyword

EQUINOX has since been adopted by Hanisch et al. (2001) which deprecates EPOCH.

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... property

In fact, apart from being conformal, the Littrow projection of 1833 goes further in allowing direct measurement of the azimuth from any point on the map to any point on the central meridian. However, this was only discovered much later, by Weir in 1890.

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... projection

The gnomonic projection is the oldest known, dating to Thales of Miletus (ca. 624-547  B.C.). The stereographic and orthographic date to Hipparchus (ca. 190-after 126  B.C.).

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...TAN

Referring to the dependence of $R_{\theta}$ on the angular separation between the tangent point and field point, i.e. the native co-latitude.

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... projection

First noted by astronomer Edmond Halley (1656-1742).

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...SIN

Similar etymology to TAN.

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... projection

Devised in 1861 by astronomer royal George Biddell Airy, 1801-1892.

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... Lambert's

The mathematician, astronomer and physicist Johann Heinrich Lambert (1728-1777) was the first to make significant use of calculus in constructing map projections. He formulated and gave his name to a number of important projections as listed in Table A.1.

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... projection

Although colloquially referred to as "Cartesian'', Claudius Ptolemy (ca. 90-ca. 170  A.D.), influential cartographer and author of the Ptolemaic model of the solar system, credits Marinus of Tyre with its invention in about A.D. 100, thus predating Descartes by some 1500 years.

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... solution

Gerardus Mercator (1512-1594), a prominent Flemish map-maker, effectively solved this equation by numerical integration. Presented in 1569 it thus predates Newton's theory of fluxions by nearly a century.

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... Sanson-Flamsteed

Nicolas Sanson d'Abbeville (1600-1667) of France and John Flamsteed (1646-1719), the first astronomer royal of England, popularized this projection, which was in existence at least as early as 1570.

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... projection

Presented in 1805 by astronomer and mathematician Karl Brandan Mollweide (1774-1825).

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... Hammer-Aitoff

David Aitoff (1854-1933) developed his projection from the zenithal equidistant projection in 1889 and in 1892 Ernst Hammer (1858-1925) applied his idea more usefully to the zenithal equal area projection. See Jones (1993).

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... projection

The ancestry of this important projection may be traced back to Ptolemy. Attribution for its invention is uncertain but it was certainly used before the birth of Rigobert Bonne (1727-1795) who did much to popularize it.

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... projections

Polyhedral projections date from renaissance times when the artist and mathematician Albrecht Dürer (1471-1528) described, although did not implement, the tetrahedral, dodecahedral, and icosahedral cases. Snyder (1993) traces subsequent development into the twentieth century, including one by R. Buckminster Fuller onto the non-Platonic "cuboctahedron'' with constant scale along each edge.

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