## Trigonometry, Plane and Spherical: With the Construction and Application of Logarithms |

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### Common terms and phrases

AC by Theor AC—BC adjacent Angle Angle ABC Angle ACB BD be drawn bisecting Chord Circle Co-f Co-s Co-sine BC Co-tangent of Half common Logarithm Corollary Degrees Diameter dius E. D. Prop equal to Half Excess Extremes fame ference find the Sine Fourth-proportional garithms given Number gles Great-Circles half the Base half the Difference Half the Sum half the vertical half this Angle Hence hyperbolic Logarithm Hypothenuse AC known Leg BC let BD manifest Moreover opposite Angle passing thro pendicular perpendicular plane Triangle ABC Proportion Radius right-angled spherical Triangle Right-line s1nce Secant Sides AC Sine BCD Sine of half spherical Angle spherical Triangle ABC subtracted supposed Table Tang Tangent of Half Tbeor Terms Theorem Trigonometry Unity versed Sine vertical Angle whence

### Popular passages

Page 1 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees; and each degree into 60 minutes, each minute into 60 seconds, and so on.

Page 3 - Canon, is a table showing the length of the sine, tangent, and secant, to every degree and minute of the quadrant, with respect to the radius, which is expressed by unity or 1, with any number of ciphers.

Page 78 - Patron," 1 740, 4to. Soon after the publication .of this book he was chosen a member of the Royal Academy at Stockholm. Our author's next work appeared in 1742, 8vo, " The Doctrine of Annuities and Reversions deduced from general and evident Principles : with useful' Tables, shewing the values of single and joint lives, &c. at different rates of interest,

Page 6 - In every plane triangle, it will be, as the sum of any two sides is to their difference...

Page 41 - The sum of the logarithms of any two numbers is equal to the logarithm of their product. Therefore, the addition of logarithms corresponds to the multiplication of their numbers.

Page 13 - If the sine of the mean of three equidifferent arcs' dius being unity) be multiplied into twice the cosine of the common difference, and the sine of either extreme be deducted from the product, the remainder will be the sine of the other extreme. (B.) The sine of any arc above 60°, is equal to the sine of another arc as much below 60°, together with the sine of its excess above 60°. Remark. From this latter proposition, the sines below 60° being known, those of arcs above 60° are determinable...

Page 31 - ... is the tangent of half the vertical angle to the tangent of the angle which the perpendicular CD makes with the line CF, bisecting the vertical angle.

Page 73 - BD, is to their Difference ; fo is the Tangent of half the Sum of the Angles BDC and BCD, to the Tangent of half their Difference.

Page 28 - As the sum of the sines of two unequal arches is to their difference, so is the tangent of half the sum of those arches to the tangent of half their difference : and as the sum...

Page 68 - In any right lined triangle, having two unequal sides ; as the less of those sides is to the greater, so is radius to the tangent of an angle ; and as radius is to the tangent of the excess of...