A history of Greek mathematics - Wilbourhall.org

BEGINNINGS OF TRIGONOMETRY 253
forms ' liber aggregativus ' and
'
liber cle principiis universalibus'.
Each of these expressions may well mean the work
of Apollonius which Marinus refers to as the ' General
Treatise ' (fj kccOoXov wpayfjiaTeia). There is no apparent
reason to doubt that the remark in question was really
contained in Menelaus's original work ; and, even if it is an
Arabian interpolation, it is not likely to have been made
without some definite authority. If then Apollonius was the
discoverer of the proposition, the fact affords some ground for
thinking that the beginnings of trigonometry go as far back,
at least, as Apollonius. Tannery 1 indeed suggested that not
only Apollonius but Archimedes before him may have compiled
a ' table of chords ', or at least shown the way to such
a compilation, Archimedes in the work of which we possess
only a fragment in the Measurement of a Circle^ and Apollonius
in the cdkvtoklov, where he gave an approximation to the value
of tt closer than that obtained by Archimedes; Tannery
compares the Indian Table of Sines in the Surya-Siddhdnta,
where the angles go by 24ths of a right angle (l/24th = 3° 45',
2/24ths=7° 30', &c), as possibly showing Greek influence.
This is, however, in the region of conjecture ; the first person
to make systematic use of trigonometry is, so far as we know,
Hipparchus.
Hipparchus, the greatest astronomer of antiquity, was
born at Nicaea in Bithynia. The period of his activity is
indicated by references in Ptolemy to observations made by
him the limits of which are from 161 B.C. to 126 B.C. Ptolemy
further says that from Hipparchus's time to the beginning of
the reign of Antoninus Pius (a.d. 138) was 265 years. 2 The
best and most important observations made by Hipparchus
were made at Rhodes, though an observation of the vernal
equinox at Alexandria on March 24, 146 B.C., recorded by him
may have been his own. His main contributions to theoretical
and practical astronomy can here only be indicated in the
briefest manner.
1
Tannery, Recherches sur Vhist. de Vastronomie ancienne, p. 64.
2 Ptolemy, Syntaxis, vii. 2 (vol. ii, p. 15).