. 800 feet. 900 feet. 1000 ft 699-97699-89699-76 :699-57 i699-33 I699-04698-69 j698-30 !697-84 I697-84 I696-78 696-17 695-50 i694-79694-02693-20 I692-32691-40690-42 I639-39 i638-30 687-17 i685-93 i684-75 1683-46632-13680-73679-29677-79676-25674-66673-01 799-96799-84799-64799-86799-00798-56798-04797-44796-76796-01795-lT794-25798-26792-18791-03789-80788-49787-11785-64784-10782-48780-79779-01777-16775-24773-26771-16769-01766-79764-49762-12769-67 899-94 899-77899-49899-09898-57897-95897-20896-35895-33894-80893-10891-80 888-85887-21885-45
. 800 feet. 900 feet. 1000 ft 699-97699-89699-76 :699-57 i699-33 I699-04698-69 j698-30 !697-84 I697-84 I696-78 696-17 695-50 i694-79694-02693-20 I692-32691-40690-42 I639-39 i638-30 687-17 i685-93 i684-75 1683-46632-13680-73679-29677-79676-25674-66673-01 799-96799-84799-64799-86799-00798-56798-04797-44796-76796-01795-lT794-25798-26792-18791-03789-80788-49787-11785-64784-10782-48780-79779-01777-16775-24773-26771-16769-01766-79764-49762-12769-67 899-94 899-77899-49899-09898-57897-95897-20896-35895-33894-80893-10891-80 888-85887-21885-45883-58881-61879-52877-32875-02872-61870-08867-458&4-72861-90853-98855-87852-72849-45846-09842-62 999-92 999-69 999-30 I 993-75 I 998-05 i 997-18 ! 996-15 994-98 993-65 992-17 i 990-52 988-73 986-78 934-68 982-42 ! 979-99 I 977-46 i 974-75 971-89 : 968-87 965-72 962-42 958-96 955-3T 951-63 947-75 943-71 939-54 935-23 930-78 926-20 921-4t Tables of Vkuskd. Sim-:s and Extekxal Secants. 415 TABLES OF NATURAL AND LOGARITHMIC VERSED SINES,AND EXTERNAL On the Construction of the Tables of Versed Sines and ExternalSecants. In tlie above figure it is required to find the value of versed sineF B = C G, of arc B C = A B angle a, and of external secant C D interms of sine C F and tangent B I). The chord B C = 2 sine ^ B C, and angle F C B is measured hyI arc AB =^ arc BC. Therefore making chord B C radius, B F will be the sine of angleF CB, and we have: Versed sine B F = 2 x sine FC B =2 x (sine ^ a)l That is, twice the square of sine of half given arc = versed C F radius. B F becomes tangent, and we liave, versedsine B F = CF x tangent F CB, or sine a x tangent ^ a. Now by similar triangles v. s. a : ex. sec. a :: cos. a : radius; find V. s. a : ex. sec. a :: sine a : tangent a; or, ex. sec. a =: y. s. a x radius ) , . _^„. i ^ - J- = tan. a x tangent | a. cosine a )Then log. v. = log. sine a + log. tan. | a — (10 = log. of R.),and log. ex. sec. a = log. v. s
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Keywords: ., bookcentury1800, bookdecade1850, booksubjectenginee, bookyear1856
