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 ... |
From inside the book
Results 6-10 of 11
Page 57
... tabular radius , ac the tabular secant of A , and be the tabular tangent of A ; ac : AC :: bc : BC , that is , Sec A : AC :: Tan A : BC . ac : AC :: ab : AB Sec A : AC :: R : AB . In Fig . 16 , where be is the tabular radius , ac the ...
... tabular radius , ac the tabular secant of A , and be the tabular tangent of A ; ac : AC :: bc : BC , that is , Sec A : AC :: Tan A : BC . ac : AC :: ab : AB Sec A : AC :: R : AB . In Fig . 16 , where be is the tabular radius , ac the ...
Page 58
... radius . As in every proportion , the three first terms must be given , to enable us to find the fourth , it is ev ... tabular radius is in the first term , we have only to add the other two terms , and then take 10 from the index ...
... radius . As in every proportion , the three first terms must be given , to enable us to find the fourth , it is ev ... tabular radius is in the first term , we have only to add the other two terms , and then take 10 from the index ...
Page 59
... radius , be will be the tabular sine of A , and ab the tabular sine of C. ( Art . 124. ) To find the perpendicular , then , by Theorem I , we have this proportion ; ac : AC :: bc : BC . Or R : AC :: Sin ABC . Whenever the terms Radius ...
... radius , be will be the tabular sine of A , and ab the tabular sine of C. ( Art . 124. ) To find the perpendicular , then , by Theorem I , we have this proportion ; ac : AC :: bc : BC . Or R : AC :: Sin ABC . Whenever the terms Radius ...
Page 64
... Radius To the base 284 So is the Secant of A 34 ° 4 ′ To the hypothenuse 342.84 10 . 2.45332 10.08177 2.53509 Making ... tabular sines , tangents , and secants . But , when any two sides of a right angled triangle are given . the ...
... Radius To the base 284 So is the Secant of A 34 ° 4 ′ To the hypothenuse 342.84 10 . 2.45332 10.08177 2.53509 Making ... tabular sines , tangents , and secants . But , when any two sides of a right angled triangle are given . the ...
Page 68
... tabular sines . But the proportion will be the same , if the sines be adapted to any other radius . ( Art.119 . ) THEOREM II . 144. In a plane triangle , As the sum of any two of the sides , To their difference ; So is the tangent of ...
... tabular sines . But the proportion will be the same , if the sines be adapted to any other radius . ( Art.119 . ) THEOREM II . 144. In a plane triangle , As the sum of any two of the sides , To their difference ; So is the tangent of ...
Other editions - View all
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.