## Elements of plane trigonometry: In which is introduced, a dissertation on the nature and use of logarithms |

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absciss arc is greater arc is less asymptotic area axis becomes equal cafe chord circular arch circumference consequently Corol cosine curvature decimal fraction diameter difference double arc draw equations extreme arc fame proportion figures fluxion follows fore foregoing former garithms given ratio hyperbola hyperbolic sector hyperbolic space infinitely small infinitum instance latter lesser loga logarithmic curve magnitude mean arc mixt numbers mixtilinear area modulus multiple arc number corresponding ordinates parallelogram perpendicular polygon portion Prop quadrant quadruple arc quantity quintuple arc radius radius of curvature rectangle regular polygon right angle right line rithms secant semicircle septuple arc serieses shewn simple arc subtangent subtract system of logarithms tangent tions tis evident triangle triple arc unity velocity versed sine whatsoever whence whole circle whole numbers

### Popular passages

Page 5 - Arc is the Difference thereof from a Quadrant. A Chord or Subtenfe, is a Right Line drawn front one End of the Arc to the other. The Right Sine of any Arc, which is'alfe commonly failed only a Sine, is a Right Line drawn, from one End ' of an Arc, perpendicular to the Radius drawn thro' the ether End of the Jaid Arc ; and is therefore the Semifubtenfe of double the Arc ; viz.

Page 7 - The sine of any arc is equal to half the chord of double the arc. Let the arc PB be double of PA. Join OA, PB intersecting each other in E.

Page 22 - So. the cosine of the mean arc, as the sine of the difference is to the difference of the sines of the extremes. For we have CD : CK : : FO : FM ; whence by doubling the...

Page 173 - He hath left us alfo his attempts upon the circle : He proved that a circle is equal to a right-angled triangle whofe bafe is equal to the circumference and its altitude equal to the radius ; and confequently that its area is...

Page 74 - The tangent of the fum of two angles is to the fum of their tangents, as the fquare of the radius to the fquare of the radius diminished by the rectangle under the tangents : And the...

Page 428 - ... •value exaft to twenty decimal places of figures, there would be occafion for no lefs than five thoufand millions of its terms, to compute which would take up above a thoufand years. Now in this extreme cafe Mr. Maferes has...

Page 37 - A /'/, the more are the Terms of the Series required to have the Sine in Numbers true to a given Place of Figures. And then when the Arc is nearly Equal to the Radius, the Series Converges very flow. And therefore, to remedy this, I have devifed other Series...

Page 6 - DEF. 11. The Cotangent of an arc is a line touching the circle at the end of the first quadrant and meeting the radius produced through the end of the arc. Thus, if IBI...

Page 170 - ... the bafe, as the fquare of the radius to the fquare of the co-fine of half the angle included between the two fides of the triangle.

Page 39 - Cofinewill become Radius, or I. And hence, if the Terms wherein a is, are taken away, and i be put inftead of b, the Series will become Newtonian.