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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Page 11
... give the numbers to four places of figures only . * In Taylor's , Hutton's and other tables , four figures are placed in the left hand column , and the fifth at the top of the page . But by the table , the log . of 21720 THE LOGARITHMIC ...
... give the numbers to four places of figures only . * In Taylor's , Hutton's and other tables , four figures are placed in the left hand column , and the fifth at the top of the page . But by the table , the log . of 21720 THE LOGARITHMIC ...
Page 19
... gives −2 for the index of the sum . Multiply Into .00845 1068 . 3.92686 or 7.92686 3.02857 3.02857 Product 9.0246 0.95543 0.95543 The product of 0.0362 into 25.38 of 0.00467 into . 348.1 is 0.9188 is 1.625 * of 0.0861 into 0.00843 is ...
... gives −2 for the index of the sum . Multiply Into .00845 1068 . 3.92686 or 7.92686 3.02857 3.02857 Product 9.0246 0.95543 0.95543 The product of 0.0362 into 25.38 of 0.00467 into . 348.1 is 0.9188 is 1.625 * of 0.0861 into 0.00843 is ...
Page 22
... gives - 3 for the in- dex of the difference of the logarithms . Divide 6.832 0.93455 Divide 0.00634 3.80209 By ⚫0362 2.55871 By 62.18 1.79365 Quot . 188.73 2.27584 Quot . 0.000102 4.00844 The quotient of 0.0985 divided by 0.007241 , is ...
... gives - 3 for the in- dex of the difference of the logarithms . Divide 6.832 0.93455 Divide 0.00634 3.80209 By ⚫0362 2.55871 By 62.18 1.79365 Quot . 188.73 2.27584 Quot . 0.000102 4.00844 The quotient of 0.0985 divided by 0.007241 , is ...
Page 30
... gives the same result as the first . But it is unnecessary , first to add two of the terms , and then the arithmetical complement of the oth- The three may be added at once ; and it will generally be expedient , to place the terms in ...
... gives the same result as the first . But it is unnecessary , first to add two of the terms , and then the arithmetical complement of the oth- The three may be added at once ; and it will generally be expedient , to place the terms in ...
Page 50
... gives 14 ° 43 ' 10 " for the answer . which added to 14 ° 43 ' 3. What is the angle belonging to the cosine 9.09773 ? Cosine next greater 82 ° 48 ' 9.09807 Next less 82 ° 49 ′ 9.09707 Given cosine 9.09773 Next less 9.09707 Difference ...
... gives 14 ° 43 ' 10 " for the answer . which added to 14 ° 43 ' 3. What is the angle belonging to the cosine 9.09773 ? Cosine next greater 82 ° 48 ' 9.09807 Next less 82 ° 49 ′ 9.09707 Given cosine 9.09773 Next less 9.09707 Difference ...
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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.