The Elements. Of Plain and Spherical Trigonometry: Also a Short Treatise of the Nature and Arithmetick of Logarithms. By Doctor John Keil, ... |
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The Elements of Plain and Spherical Trigonometry: Also a Short Treatise of ... John Keill No preview available - 2017 |
The Elements of Plain and Spherical Trigonometry: Also a Short Treatise of ... John Keill No preview available - 2017 |
Common terms and phrases
alfo alſo Ambiguous Angle BCD Arch Azimuth Bafe becauſe bifected Cafe Circle Cofine Complement confequently Coroll Difference diftant Diſtance drant Ecliptic Equi equiangular Equinoctial expreffing faid fame Affection fecond feven fhall be equal fhews fince firft Term firſt fome fometimes fought Fraction fubtracted fuppofed garithm given gles Globe greater half Horizon Hypothenufe Index Intereft Latitude lefs Legs A B likewife Loga Logarithm of Unity mean Proportionals Meaſure Meridian muſt Neper Number o's Pofition Obtufe Perpendicular falls Place from Unity Places of Figures Pole Prime Vertical Prop PROPOSITION Quadrant Quadrant of Altitude Quotient Radius Ratio Rectangle reprefented Right Angles Right Lines rithm Root Secant Semicircle ſhall Sides BC Spherical Triangle Star Subtangent Tangent thefe thereof theſe thofe thoſe Trigonometry Verfed Sine Whence Wherefore whofe
Popular passages
Page 10 - If the sines of all arcs, from the beginning of a quadrant to any part of a quadrant, distant from each other by a given interval, be given, thence we may find the sines of all arcs to the double of that part. For example: let all the sines to 15 degrees be given; then, by the preceding analogy, all the sines to 30 degrees may be found.
Page 26 - ... 2. The pole of a great circle of a sphere is a point in the superficies of the sphere, from which all strai Tht lines drawn to the circumference of the circle are equal.
Page 10 - So, likewise, may the sines of the minutes in the beginning of the quadrant be found, by having the sines and cosines of one and two minutes given. For, as the radius is to double the cosine of 2' : : sine 1' : difference of the sines of 1' and 3 : : sine 2' : difference of the sines of 0" and 4'; that is, to the sine of 4'.
Page 14 - Whence, if the sines of one and two minutes be given, we may easily find all the other sines in the following manner. Let the cosine of the arc of one minute, that is, the sine of the arc of 89 deg. 59', be called Q; and make the following analogies ; R : 2 Q : : Sin. 2' : S. 1' + S. 3'. Wherefore the sine of 3 minutes will be given1 Also, R. : 2 Q : : S. 3' : S. 2' + S. 4'. Wherefore the S. 4
Page 22 - It is alfo manifeft from 32. i. that if one of the acute angles of a rightangled triangle be given, the other is alfo given, for it is the complement of the former to a right angle. If two angles of any triangle be given, the third is alfo given, being the fupplement of the two given angles to two right angles.
Page 15 - And in like manner, the sines of every minute of the quadrant will be given. And because the radius, or the first term of the analogy, is unity, the operations will be with great ease and expedition calculated by multiplication, and contracted by addition. When the sines are found to 60 degrees, all the other sines may be had by addition only, by Cor. 1. Prop. 6. The sines being given, the tangents and secants may be found from the following analogies...
Page 97 - Logarithms are continued but to io Places of Figures. Mr. Briggs alfo has calculated the Logarithms of the Sines and Tangents of every Degree, and the hundredth Parts of Degrees to...
Page 10 - Degrees ; fo alfo is the Sine of 3 Degrees, to the Difference between the Sines of 12 and 18 Degrees ; and fo on continually until you come to the Sine of 30 Degrees. After the fame...