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Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin( α + β ) = sin α cos β + cos α sin ...
The kezayit is, by different sources, considered equal to 1 ⁄ 2 a beitza, 1 ⁄ 3 of a beitza, or not directly related to the other units of volume. The omer, which the Torah mentions as being equal to one-tenth of an ephah, [30] is equivalent to the capacity of 43.2 eggs, or what is also known as one-tenth of three seahs. [31]
The se'ah or seah (Hebrew: סאה sə’āh), plural se'im, is a unit of dry measure of ancient origin found in the Bible and in Halakha (Jewish law), which equals one third of an ephah, or bath. In layman's terms, it is equal to the capacity of 144 medium-sized eggs, or what is equal in volume to about 9 US quarts (8.5 litres). [1]
From earliest Sumerian times, a mina was a unit of weight. At first, talents and shekels had not yet been introduced. By the time of Ur-Nammu (shortly before 2000 BCE), the mina had a value of 1 ⁄ 60 talent as well as 60 shekels.
There are several equivalent ways for defining trigonometric functions, and the proofs of the trigonometric identities between them depend on the chosen definition. The oldest and most elementary definitions are based on the geometry of right triangles and the ratio between their sides.
It is used in the Bible as an ancient unit of volume for grains and dry commodities, and the Torah mentions it as being equal to one tenth of an ephah. [2] According to the Jewish Encyclopedia (1906), an ephah was defined as being 72 logs , and the Log was equal to the Sumerian mina , which was itself defined as one sixtieth of a maris ; [ 3 ...
The quantity 206 265 ″ is approximately equal to the number of arcseconds in a circle (1 296 000 ″), divided by 2π, or, the number of arcseconds in 1 radian. The exact formula is = (″) and the above approximation follows when tan X is replaced by X.
In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that ...