. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . mon logm = Napierian logm x .43429448. The number .43429448 is called the modulus of the commonsystem. It is usually denoted by /a. Hence, the common logarithm of any number is equal tothe Napierian logarithm of the same number multiplied bythe modulus of the common system, .43429448. Multiplying (4) of Art. 130 by /*, we obtain a series bywhich common logarithms may be computed; thus, logioO + l) = 1,1 1 log10n + 2fx _2n + l 3(2n + l)3 + 5(2n + l) : + -] (1) Common Logarit
. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . mon logm = Napierian logm x .43429448. The number .43429448 is called the modulus of the commonsystem. It is usually denoted by /a. Hence, the common logarithm of any number is equal tothe Napierian logarithm of the same number multiplied bythe modulus of the common system, .43429448. Multiplying (4) of Art. 130 by /*, we obtain a series bywhich common logarithms may be computed; thus, logioO + l) = 1,1 1 log10n + 2fx _2n + l 3(2n + l)3 + 5(2n + l) : + -] (1) Common = /xloge2 = .43429448 x .69314718 = . = /xloge3 = .43429448 x = . = 21og102 = .6020600. log105 = /xloge5 = .43429448 x = . so on. 132. If 6 be the Circular Measure of an Acute Angle,sin 9, 6, and tan 0 are in Ascending Order of Magnitude. With centre O, and any radius, de-scribe an arc BAB. Bisect the angleBOB by OA; join BB, and draw thetangents BT, BT. Let AOB = AOB = ft Then BB < arc BAB < BT + BT (Geom., Art. 246).-. BC<arcBA< LIMITING VALUES OF SIN6. 209 BC BA BT OB OB OB* .-. sin 6 < 6 < tan 6. 133. The Limit of ^^-, when 6 is Indefinitely Diminished,is Unity. We have sin 6 < 6 < tan 6 (Art. 132) .-. l<-i-< sec^ (Art. 132) . 0^ 6 6 .-. sin->-cos--2 2 2 210 PLANE TRIGONOMETRY. 0 B 8 .-. 2 sin-cos- >0cos2-- 2 2 2
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Keywords: ., bookcentury1900, bookdecade1900, booksubjecttrigono, bookyear1902
