A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of the Nature and Use of Logarithms. Being the Second Part of A Course of Mathematics, Adapted to the Method of Instruction in the American Colleges ...Howe & Deforest, 1815 - 126 páginas |
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Página 38
... gles 360 ° ; and in any other angle , as many degrees , as in the arc by which it is subtended . 76. The sum of the three angles of any triangle being equal to two right angles , ( Euc . 32. 1. ) is equal to 180 ° . Hence , there can ...
... gles 360 ° ; and in any other angle , as many degrees , as in the arc by which it is subtended . 76. The sum of the three angles of any triangle being equal to two right angles , ( Euc . 32. 1. ) is equal to 180 ° . Hence , there can ...
Página 41
... gles is the complement of the other ; ( Art . 77. ) the sine , tan- gent , and secant of one of these angles , are the cosine , co- tangent , and cosecant of the other . 90. The sine , tangent , and secant of the supplement of an angle ...
... gles is the complement of the other ; ( Art . 77. ) the sine , tan- gent , and secant of one of these angles , are the cosine , co- tangent , and cosecant of the other . 90. The sine , tangent , and secant of the supplement of an angle ...
Página 47
... gles less than 45o , and v . v . Now , to bring the trigonometrical tables within a small compass , the same column is made to answer for the sines of a number of angles above 45 ° , and for the cosines of an equal number below 45 ...
... gles less than 45o , and v . v . Now , to bring the trigonometrical tables within a small compass , the same column is made to answer for the sines of a number of angles above 45 ° , and for the cosines of an equal number below 45 ...
Página 67
... gles may be calculated by the following the- orems . THEOREM I. In any plane triangle , the sines of the angles are as their op- posite sides . Let the angles be denoted by the letters A , B , C , and their opposite sides by a , b , c ...
... gles may be calculated by the following the- orems . THEOREM I. In any plane triangle , the sines of the angles are as their op- posite sides . Let the angles be denoted by the letters A , B , C , and their opposite sides by a , b , c ...
Página 70
... gles . For , in the right angled triangles ACP and BCP , ( Fig . 26. ) if CP be made radius , ( Art . 126. ) R : PC :: Tan ACP : AP R : PC :: Tan BCP : BP Therefore , by equality of ratios , ( Alg . 364. * ) Tan ACP : AP :: Tan BCP : BP ...
... gles . For , in the right angled triangles ACP and BCP , ( Fig . 26. ) if CP be made radius , ( Art . 126. ) R : PC :: Tan ACP : AP R : PC :: Tan BCP : BP Therefore , by equality of ratios , ( Alg . 364. * ) Tan ACP : AP :: Tan BCP : BP ...
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Términos y frases comunes
acute angle added angle ACB arithmetical complement arithmetical progression b+sin base calculation centre circle cosecant Cosine Cotangent Tangent decimal degrees and minutes divided division divisor equal to radius equation errour exponents extend find the angles find the logarithm fraction geometrical progression given angle given number given side Given the angle gles greater half the sum hypothenuse JEREMIAH DAY length less line of chords line of numbers lines of sines loga logarithmic sine logarithmic TANGENT metical Mult multiplied natural number natural sines number of degrees opposite angles perpendicular positive proportion quadrant quotient radix right angled triangle rithms root secant similar triangles sine of 30 sines and cosines slider square subtracting tables tabular radius tabular sine tangent of half theorem transverse distance triangle ABC trigonometrical tables Trigonometry versed sine vulgar fraction
Pasajes populares
Página 68 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Página 42 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Página 105 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Página 49 - ... at the head of the column, take the degrees at the top of the table, and the minutes on the left; but if the title be at the foot of the column, take the degrees at the bottom, and the minutes on the right.
Página 39 - With these the learner should make himself perfectly familiar. 82. The SINE of an arc is a straight line drawn from one end of the arc, perpendicular to a diameter which passes through the other end. Thus BG (Fig.
Página 116 - In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Página 37 - The periphery of every circle, whether great or small, is supposed to be divided into 360 equal parts called degrees, each degree into 60 minutes, each minute into 60 seconds, each second into 60 thirds, &c., marked with the characters °, ', ", '", &c. Thus, 32° 24...
Página 72 - ... angle. The third angle is found by subtracting the sum of the other two from 180° ; and the third side is found as in Case I.