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 σελίδες |
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Σελίδα 8
... length , with the different pow- ers of a . Then the distances from A to 1 , 2 , 3 , & c . will represent the logarithms of a , a , a3 , & c . ( Art . 2. ) The line CH is called the logarithmic curve , because its abscissas are ...
... length , with the different pow- ers of a . Then the distances from A to 1 , 2 , 3 , & c . will represent the logarithms of a , a , a3 , & c . ( Art . 2. ) The line CH is called the logarithmic curve , because its abscissas are ...
Σελίδα 37
... length of the sides , and the quantity of the angles . In addition to this , from its principles are deriv- ed many interesting methods of investigation in the higher branches of analysis , particularly in physical astronomy . Scarcely ...
... length of the sides , and the quantity of the angles . In addition to this , from its principles are deriv- ed many interesting methods of investigation in the higher branches of analysis , particularly in physical astronomy . Scarcely ...
Σελίδα 38
... length ; but a certain portion of the whole circumference of any circle . It is evident , that the 360th part of a large circle is greater , than the same part of a small one . On the other hand , the number of degrees , in a small ...
... length ; but a certain portion of the whole circumference of any circle . It is evident , that the 360th part of a large circle is greater , than the same part of a small one . On the other hand , the number of degrees , in a small ...
Σελίδα 39
... length , as a unit . ( Alg . 510. ) To this must be referred the numbers expressing the lengths of other lines . Thus 20 will be twenty times the radius , and 0.75 , three fourths of the radius . Definitions of Sines , Tangents ...
... length , as a unit . ( Alg . 510. ) To this must be referred the numbers expressing the lengths of other lines . Thus 20 will be twenty times the radius , and 0.75 , three fourths of the radius . Definitions of Sines , Tangents ...
Σελίδα 40
... length ; whereas , in Trigonometry , they extend from the diameter to the point in which they intersect each other . 87. The lines just defined are sines , tangents and secants of arcs . BG ( Fig . 3. ) is the sine of the arc AG . But ...
... length ; whereas , in Trigonometry , they extend from the diameter to the point in which they intersect each other . 87. The lines just defined are sines , tangents and secants of arcs . BG ( Fig . 3. ) is the sine of the arc AG . But ...
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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
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Σελίδα 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.
Σελίδα 42 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.