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# TRIGONOMETRY BOOK PDF

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## Conditions of Use

In view of the pre-Hellenic lack of the concept of angle measure, such a study might better be called "trilaterometry", or the measure of three sided polygons trilaterals , than "trigonometry", the measure of parts of a triangle.

With the Greeks we first find a systematic study of relationships between angles or arcs in a circle and the lengths of chords subtending these.

Properties of chords, as measures of central and inscribed angles in circles, were familiar to the Greeks of Hippocrates' day, and it is likely that Eudoxus had used ratios and angle measures in determining the size of the earth and the relative distances of the sun and the moon.

In the works of Euclid there is no trigonometry in the strict sense of the word, but there are theorems equivalent to specific trigonometric laws or formulas. Propositions II. Theorems on the lengths of chords are essentially applications of the modern law of sines.

## Spherical Trigonometry: For the Use of Colleges and Schools by I. Todhunter

We have seen that Archimedes' theorem on the broken chord can readily be translated into trigonometric language analogous to formulas for sines of sums and differences of angles. In Book I of this treatise Menelaus establishes a basis for spherical triangles analogous to that of Euclid I for plane triangles.

The second book of the Sphaerica describes the application of spherical geometry to astronomical phenomena and is of little mathematical interest. Book III, the last, contains the well known "theorem of Menelaus" as part of what is essentially spherical trigonometry in the typical Greek form — a geometry or trigonometry of chords in a circle. In the circle in Fig. Menelaus and his Greek successors instead referred to AB simply as the chord corresponding to the arc AB.

Instead we have an treatise, perhaps composed earlier ca. In this work Aristarchus made the observation that when the moon is just half-full, the angle between the lines of sight to the sun and the moon is less than a right angle by one thirtieth of a quadrant.

In trigonometric language of today this would mean that the ratio of the distance of the moon to that of the sun the ration ME to SE in Fig. Functional Analysis.

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