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

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४८ AB by Theor ABC+ACB AC by Theor AC-BC adjacent Angle alfo alſo Arch Bafe Baſe becauſe biſects Cafe Chord Circle Co-f Co-fine AC Co-tangent of Half common Logarithm confequently Corol COROLLARY demonftrated Diameter E. D. PROP equal to Half Exceſs fame fince find the Sine firſt fubtracted garithms gles Great-Circles half the Difference Half the Sum half the vertical Hence hyperbolic Logarithm Hypothenuse interfect laſt Leg BC manifeſt Moreover oppofite paſſing thro pendicular perpendicular plane Triangle ABC poſed Progreſſion propoſed Radius Rectangle reſpectively right-angled spherical right-angled ſpherical Triangle Right-line ſame Secant ſhall Sides AC ſince Sine 3º Sine 59 Sine BCD Sine of half ſpherical Triangle ABC ſuppoſed Tang Tangent of Half THEOREM theſe thoſe Trigonometry verſed Sine vertical Angle whence whoſe

### 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 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...