Mollweiden.

Brit.

/ˈmɒlvʌɪdə/, U.S.

/ˈmɑlˌvaɪdə/

Origin: From a proper name. Etymon: proper name Mollweide.

Etymology: < the name of Karl B. Mollweide (1774–1825), German mathematician and astronomer, who first used the map projection (see main sense), and made famous a set of trigonometric identities (see Compounds 1, and note at that entry).

Cartography. = Mollweide projection at Compounds 2; a map drawn using Mollweide's projection. Also in the genitive, used absol.

ΚΠ

1901 C. F. Close Map Projections ii. 22 (heading) Homalographic equal-area (Mollweide's). Sometimes called Babinet's.

1912 A. R. Hinks Map Projections vii. 73 For the whole world on a single sheet we have Mollweide, which is useful for distribution diagrams, but can scarcely be called a map.

1937 F. Debenham Exercises in Cartogr. x. 118 Make an approximate graticule on the Oblique Mollweide suitable for showing the British Empire Seas.

1969 G. C. Dickinson Maps & Air Photographs i. 16 The hybrid homolosine projection—simply a sinusoidal projection between the 40° parallels and a Mollweide's beyond.

Compounds

C1. Mathematics. attributive. Designating either of two trigonometrical equations relating the angles of a triangle (A, B, and C) and the lengths of the opposite sides (a, b, and c respectively): c sin ^{A − B}/ ₂ = (a − b) cos ^C/ ₂ and c cos ^{A − B}/ ₂ = (a + b) sin ^C/ ₂.The equations were published by Mollweide in Monatl. Corresp. zur Beförderung der Erd- u. Himmels-Kunde 18 396, but had been published earlier in T. Simpson Trigonom., Plane & Spherical (1748) 59; the second equation was first published in I. Newton Arithmetica Universalis (1707) 121.

ΚΠ

c1914 E. J. Wilczynski Plane Trigonom. & Applic. vii. 104 These formulae, known as the Mollweide equations, are particularly convenient for the purpose of checking the accuracy of the numerical solution of a triangle.

c1914 E. J. Wilczynski Plane Trigonom. & Applic. vii. 105 It is not justifiable historically to call equations (6) Mollweide's equations.

1921 Amer. Math. Monthly 28 408 Professor Rusk gave..proofs for the Mollweide formulas, showing that they themselves are half-angle formulas.

1945 Amer. Math. Monthly 52 209 A longer, but sound, check can be given by using one of the Mollweide relations.

1956 Amer. Math. Monthly 62 367 Since B = 2A, C = π − 3A and (by a Mollweide equation) (a + c)/b = cos (2A − π/2)/sin A.

1989 Encycl. Brit. XXVIII. 885/1 The Gauss-Delambre and Mollweide relations (trigonometric in nature) came later, in 1807–09.

C2. Cartography. attributive and in the genitive, esp. in Mollweide projection. Designating a homalographic map projection in which the surface of the globe is represented by an ellipse, with lines of latitude represented by the major axis and straight lines parallel to it (spaced more closely towards the poles) and meridians represented by the minor axis and equally spaced elliptical curves.

ΚΠ

1921 Times Lit. Suppl. 6 Oct. 646/3 This map of the Pacific, on Mollweide's homolographic projection.

1937 F. Debenham Exercises in Cartogr. x. 118 Draw an interrupted Mollweide projection to show continental areas with the least distortion.

1947 H. D. Thompson Fund. Earth Sci. v. 52 Mollweide's Homalographic equal-area projection (1805) shows the entire surface of the earth inside an ellipse, the major, or equatorial axis of which is twice as long as the minor axis.

1960 F. Land Lang. Math. vi. 70 Mollweide's map..is an equal-area map, preserving area relations at the expense of shapes.

1971 R. W. Purton Let's look at Maps & Mapmaking 14 Mollweide's projection can be drawn with any line of longitude as its centre and can be used to draw attention to one particular part of the world.

1995 M. Monmonier Drawing Line i. 16 The Mollweide projection offers lower distortion of shape in higher latitudes because its meridians converge to a point less sharply than on the sinusoidal.

This entry has been updated (OED Third Edition, September 2002; most recently modified version published online March 2022).

单词	mollweide
释义	Mollweiden. Brit. /ˈmɒlvʌɪdə/, U.S. /ˈmɑlˌvaɪdə/ Origin: From a proper name. Etymon: proper name Mollweide. Etymology: < the name of Karl B. Mollweide (1774–1825), German mathematician and astronomer, who first used the map projection (see main sense), and made famous a set of trigonometric identities (see Compounds 1, and note at that entry). Cartography. = Mollweide projection at Compounds 2; a map drawn using Mollweide's projection. Also in the genitive, used absol. ΚΠ 1901 C. F. Close Map Projections ii. 22 (heading) Homalographic equal-area (Mollweide's). Sometimes called Babinet's. 1912 A. R. Hinks Map Projections vii. 73 For the whole world on a single sheet we have Mollweide, which is useful for distribution diagrams, but can scarcely be called a map. 1937 F. Debenham Exercises in Cartogr. x. 118 Make an approximate graticule on the Oblique Mollweide suitable for showing the British Empire Seas. 1969 G. C. Dickinson Maps & Air Photographs i. 16 The hybrid homolosine projection—simply a sinusoidal projection between the 40° parallels and a Mollweide's beyond. Compounds C1. Mathematics. attributive. Designating either of two trigonometrical equations relating the angles of a triangle (A, B, and C) and the lengths of the opposite sides (a, b, and c respectively): c sin ^{A − B}/ ₂ = (a − b) cos ^C/ ₂ and c cos ^{A − B}/ ₂ = (a + b) sin ^C/ ₂.The equations were published by Mollweide in Monatl. Corresp. zur Beförderung der Erd- u. Himmels-Kunde 18 396, but had been published earlier in T. Simpson Trigonom., Plane & Spherical (1748) 59; the second equation was first published in I. Newton Arithmetica Universalis (1707) 121. ΚΠ c1914 E. J. Wilczynski Plane Trigonom. & Applic. vii. 104 These formulae, known as the Mollweide equations, are particularly convenient for the purpose of checking the accuracy of the numerical solution of a triangle. c1914 E. J. Wilczynski Plane Trigonom. & Applic. vii. 105 It is not justifiable historically to call equations (6) Mollweide's equations. 1921 Amer. Math. Monthly 28 408 Professor Rusk gave..proofs for the Mollweide formulas, showing that they themselves are half-angle formulas. 1945 Amer. Math. Monthly 52 209 A longer, but sound, check can be given by using one of the Mollweide relations. 1956 Amer. Math. Monthly 62 367 Since B = 2A, C = π − 3A and (by a Mollweide equation) (a + c)/b = cos (2A − π/2)/sin A. 1989 Encycl. Brit. XXVIII. 885/1 The Gauss-Delambre and Mollweide relations (trigonometric in nature) came later, in 1807–09. C2. Cartography. attributive and in the genitive, esp. in Mollweide projection. Designating a homalographic map projection in which the surface of the globe is represented by an ellipse, with lines of latitude represented by the major axis and straight lines parallel to it (spaced more closely towards the poles) and meridians represented by the minor axis and equally spaced elliptical curves. ΚΠ 1921 Times Lit. Suppl. 6 Oct. 646/3 This map of the Pacific, on Mollweide's homolographic projection. 1937 F. Debenham Exercises in Cartogr. x. 118 Draw an interrupted Mollweide projection to show continental areas with the least distortion. 1947 H. D. Thompson Fund. Earth Sci. v. 52 Mollweide's Homalographic equal-area projection (1805) shows the entire surface of the earth inside an ellipse, the major, or equatorial axis of which is twice as long as the minor axis. 1960 F. Land Lang. Math. vi. 70 Mollweide's map..is an equal-area map, preserving area relations at the expense of shapes. 1971 R. W. Purton Let's look at Maps & Mapmaking 14 Mollweide's projection can be drawn with any line of longitude as its centre and can be used to draw attention to one particular part of the world. 1995 M. Monmonier Drawing Line i. 16 The Mollweide projection offers lower distortion of shape in higher latitudes because its meridians converge to a point less sharply than on the sinusoidal. This entry has been updated (OED Third Edition, September 2002; most recently modified version published online March 2022). < n.1901
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