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 ... |
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... angles ; and especially to bring distinctly into view the principle on which most trigonometrical calculations are founded , the proportion between the parts of the given tri- angle , and a similar one formed from the sines , tangents ...
... angles ; and especially to bring distinctly into view the principle on which most trigonometrical calculations are founded , the proportion between the parts of the given tri- angle , and a similar one formed from the sines , tangents ...
Page 38
... given length ; but a certain portion of the whole circumference of any circle . It is evident , that the 360th part ... angle , a circle is so described that its centre shall be the angular point , and its periphery shall cut the two lines ...
... given length ; but a certain portion of the whole circumference of any circle . It is evident , that the 360th part ... angle , a circle is so described that its centre shall be the angular point , and its periphery shall cut the two lines ...
Page 46
... angle , is the logarithm of the natural sine of that angle . The artifi- cial tangent is the logarithm of the ... given angle within the quadrant is greater than 45 ° , its * Or the tables may be supposed to be calculated to the radius ...
... angle , is the logarithm of the natural sine of that angle . The artifi- cial tangent is the logarithm of the ... given angle within the quadrant is greater than 45 ° , its * Or the tables may be supposed to be calculated to the radius ...
Page 47
... angle is less than 45 ° , its complement is greater . Hence , every co- sine , cotangent , and cosecant of an angle ... given angle is less than 45 ° , look for the degrees at the top of the table , and the minutes on the left ; then ...
... angle is less than 45 ° , its complement is greater . Hence , every co- sine , cotangent , and cosecant of an angle ... given angle is less than 45 ° , look for the degrees at the top of the table , and the minutes on the left ; then ...
Page 48
... given angle is greater than 90 ° , look for the sine , tangent , & c . of its supplement . ( Art . 98 , 99. ) The log . sine of 96 ° 44 ' is 9.99699 The cosine of 171 ° 16 ' 9.99494 The tangent of 130 ° 26 ' 10.06952 The cotangent of ...
... given angle is greater than 90 ° , look for the sine , tangent , & c . of its supplement . ( Art . 98 , 99. ) The log . sine of 96 ° 44 ' is 9.99699 The cosine of 171 ° 16 ' 9.99494 The tangent of 130 ° 26 ' 10.06952 The cotangent of ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 42 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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.