The very great importance to Elementary Euclidean Geometry of the figure intermediate between the Straight Line and the Triangle appears to have been missed: viz. of the plane figure formed by two intersecting straight lines, each unbounded both ways. For this type of figure we use the name “Complete Angle.”

Taking ABC as the triangle of reference, with the usual notation for its sides and angles, let l = s − a, m = s− b, n = s − c. Let I, I1, I2, I3 be the centres of the inscribed and escribed circles DEF, D1E1F1, D2E2F2, D3E3F3.

Through A, B, C draw parallels to the opposite sides forming the triangle A1B1C1, so that AAl, BB1, CC1 are the medians of the triangle ABC, and there are then ten triangles like ABB1, ACB1, etc., of the same area.

Ser. v. 89. John of Halifax.—Since every country has its Holywood, and de Sacnbosco does not distinguish Holywood from Halifax, John of Halifax has been claimed both by Ireland and Scotland, and, if I remember right, by some foreign countries. The manuscripts of his works, as well as the earlier printed editions, call him Anglus or Anglicus; and he lived in a time at which the natives of the three countries were as distinct as Frenchmen, Spaniards, and Italians. Bale, quoting Leland, calls him Halifax; as does Tanner: Pits gives his birth to Halifax. He was buried in the Maturin convent at Paris, where his epitaph existed in the sixteenth century. Pits implies that it appears from the epitaph that he died in 1256: Maestlinus expressly affirms that it can be collected from the epitaph, in the Ad Lectorem of his Epitome Astronorniae. All the authorities believe him to be English; and Leland thought he traced him as a student at Oxford. But had the manuscripts called him anything but English, the other evidence would not have weighed them down; for there are plenty of Holywoods, and there was, notoriously, a press of foreign students to Oxford in the thirteenth century. But name and residence in England may come in aid of the manuscripts.