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 3
... term index , as it is used here , may possibly lead to some con- fusion in the mind of the learner . For the logarithm itself is the in- dex or exponent of a power . The characteristic , therefore , is the in- dex of an index . 8. The ...
... term index , as it is used here , may possibly lead to some con- fusion in the mind of the learner . For the logarithm itself is the in- dex or exponent of a power . The characteristic , therefore , is the in- dex of an index . 8. The ...
Page 7
... term is the product of the preceding term into the ratio . But the logarithm of this product is the sum of the logarithms of the preceding term and the ratio ; that is , the logarithms increase by a common addition , and are , therefore ...
... term is the product of the preceding term into the ratio . But the logarithm of this product is the sum of the logarithms of the preceding term and the ratio ; that is , the logarithms increase by a common addition , and are , therefore ...
Page 12
... take 36840 , and 36850 , For 792674 , For 6537825 , 792600 , 6537000 , 792700 , 6538000 , & c . The first term of the proportion will then be 10 , or 100 , or 1000 , & c . Ex . 1. Required the logarithm of 362572 . The 12 THE LOGARITHMIC.
... take 36840 , and 36850 , For 792674 , For 6537825 , 792600 , 6537000 , 792700 , 6538000 , & c . The first term of the proportion will then be 10 , or 100 , or 1000 , & c . Ex . 1. Required the logarithm of 362572 . The 12 THE LOGARITHMIC.
Page 17
... term required in single and compound proportion . The principle on which all these calculations are conducted , is this ; If the logarithm of two numbers be added , the SUM will be the logarithm of the PRODUCT of the numbers ; and If ...
... term required in single and compound proportion . The principle on which all these calculations are conducted , is this ; If the logarithm of two numbers be added , the SUM will be the logarithm of the PRODUCT of the numbers ; and If ...
Page 27
... term in a propor- tion , ADD the logarithms of the SECOND and THIRD terms , and from the sum SUBTRACT the logarithm of the FIRST term . The remainder will be the logarithm of the ... term Third term 378 2.57749 LOGARITHMS . 27 Proportion.
... term in a propor- tion , ADD the logarithms of the SECOND and THIRD terms , and from the sum SUBTRACT the logarithm of the FIRST term . The remainder will be the logarithm of the ... term Third term 378 2.57749 LOGARITHMS . 27 Proportion.
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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.