> as lemmas

1600 Abp. G. Abbot Expos. Prophet Ionah xviii. 387 Those come within this compasse, who do tye the euent of things to Pythagorean numbers, as the chaunges of states and kingdomes to the ends of seuen yeares, and of nine yeares, being multiplied vp and downe.

1757 G. Colman Connoisseur (ed. 2) IV. 100 The mystery..was as dark and unfathomable as the Pythagorean number, or the secret doctrines of Trismegist.

1858 W. Whewell Hist. Sci. Ideas i. ii. 77 Things shared the nature of the Platonic Ideas ‘by participation’, while they shared the nature of Pythagorean Numbers ‘by imitation’.

1879 Scribner's Monthly Apr. 896/1 Twelve is the Pythagorean number of man and humanity.

1912 Science 7 June 880/1 Pythagoras gave a general rule by means of which one can find any desired number of such solutions, and hence these triplets are often called Pythagorean numbers.

1929 Amer. Math. Monthly 36 286 Consecutive rectangular triangles..each having for its sides the Pythagorean numbers h, (h²−1)/2, (h²+1)/2, where h is the hypotenuse of the preceding triangle [etc.].

1984 Coll. Math. Jrnl. 15 325 Although the problem of constructing quadruples of Pythagorean numbers might seem harder and more complicated than the original task of finding Pythagorean triples, it is easier to solve the equation with four unknowns x² + y² + z² = w².

1996 S. H. Nasr Relig. & Order of Nature iii. 83 Pythagorean mathematics was a means of uniting rather than dividing, and Pythagorean numbers and geometric patterns are so many reflections of Unity.