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 38
... subtended by an arc of 90 ° , the angle itself is said to contain 90 ° . Hence , in two right angles , there are 180 ° , in four right an- gles 360 ° ; and in any other angle , as many degrees , as in the arc by which it is subtended ...
... subtended by an arc of 90 ° , the angle itself is said to contain 90 ° . Hence , in two right angles , there are 180 ° , in four right an- gles 360 ° ; and in any other angle , as many degrees , as in the arc by which it is subtended ...
Page 40
... subtends the angle GCA . BG is then the sine of the arc which subtends the angle GCA . This is more concisely ... subtended by the arc . Whenever , therefore , the sine , tangent , or secant of an an- gle is spoken of ; we are to ...
... subtends the angle GCA . BG is then the sine of the arc which subtends the angle GCA . This is more concisely ... subtended by the arc . Whenever , therefore , the sine , tangent , or secant of an an- gle is spoken of ; we are to ...
Page 43
... subtended by the equal sides CA and CS , both radii of the circle . Each , therefore , is equal to half 120 ° , that is , to 60 ° . All the angles being equal , the sides are equal , and therefore AS , the chord of 60 ° , is equal to CS ...
... subtended by the equal sides CA and CS , both radii of the circle . Each , therefore , is equal to half 120 ° , that is , to 60 ° . All the angles being equal , the sides are equal , and therefore AS , the chord of 60 ° , is equal to CS ...
Page 73
... subtended by the latter , will necessarily be acute . For there can be but one obtuse angle in a triangle , and this is always subtended by the long- est side . ( Art . 149. ) If the given angle be obtuse , the other two will , of ...
... subtended by the latter , will necessarily be acute . For there can be but one obtuse angle in a triangle , and this is always subtended by the long- est side . ( Art . 149. ) If the given angle be obtuse , the other two will , of ...
Page 114
... subtend- ing the angle is greater , or less , than a right angle . ( Euc . 12 , 13. 2. ) : NOTE H. p . 76 . SOLUTIONS OF TRIANGLES . Any triangle whatever may be solved , by the theorems in section IV . But there are other methods , by ...
... subtend- ing the angle is greater , or less , than a right angle . ( Euc . 12 , 13. 2. ) : NOTE H. p . 76 . SOLUTIONS OF TRIANGLES . Any triangle whatever may be solved , by the theorems in section IV . But there are other methods , by ...
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Common terms and phrases
acute angle added angle ACB arithmetical complement arithmetical progression b-sin b+sin base calculation centre chord of 60 circle cosecant 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 Prod proportion quadrant quotient radix right angled triangle rithms root secant similar triangles Sine Tangent Cotangent sines and cosines slider square subtended 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.