History of trigonometry

"The development of Indian trigonometry, based on sine as against chord of the Greeks was another of s achievements which was necessary for astronomical calculations. Because of his own concise notation, he could express the full sine table in just one couplet, which students could easily remember. For preparing the table of sines, he gave two methods, one of which was based on the property that the second order sine differences were proportional to sines themselves."

"[W]hat else... the reason of doubts arising in solutions... of plane and spherical triangles, but the want of accurate determinations and explanations?"

"[T]o what can this be owing, but to the want of sufficient principles, the neglect of enumerating and distinguishing: cases of a proposition, and the inattention to rendering the subject as complete as possible?"

"[T]here is as yet no classical book of Trigonometry in any language... fit to give to learners a solid foundation in them... as are Euclids Elements, Archimedes de Sphaera et Cylindro, and Dr. Hamiltons Conic Sections."

"[T]he reason, why in Algebra and Fluxions, expressions for trigonometrical lines always run out into infinite series... is because the number of arches, to which any one of such lines belongs is always infinite."

"The British mathematicians have been the greatest, nay... the only improvers of Trigonometry within these two centuries. ...[N]ot to mention the extraordinary inventions of Lord Neper... nor the analogies, wherein sines and tangents of half-arches are used, nor the applications of Trigonometry to of the sphere, for all which we are indebted... the very words of Trigonometry, cosine, cotangent, &c. have been first used by the writers of that nation."