Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 páginas |
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Página 11
... less of the proposed sides ( Ab or AB ) is to the greater ( AC ) , so is radius to the tangent of an angle ( AbC , see Theor . 2. ) And as radius to the tangent of the excess of this angle above 45 ° , so is the tangent of half the sum ...
... less of the proposed sides ( Ab or AB ) is to the greater ( AC ) , so is radius to the tangent of an angle ( AbC , see Theor . 2. ) And as radius to the tangent of the excess of this angle above 45 ° , so is the tangent of half the sum ...
Página 14
... less than the given side BC , ad- jacent to it ( except the angle found be exactly a right one ) : for then another right line Ba , equal to BA , may be drawn from B to a point in the base , somewhere between C and the perpendicular BD ...
... less than the given side BC , ad- jacent to it ( except the angle found be exactly a right one ) : for then another right line Ba , equal to BA , may be drawn from B to a point in the base , somewhere between C and the perpendicular BD ...
Página 21
... less than de- grees and minutes is regarded ) , may be effected by barely taking the proportional parts of the differences . But if a greater degree of accuracy be insisted on , and you would have a table carried on to 7 or 8 places ...
... less than de- grees and minutes is regarded ) , may be effected by barely taking the proportional parts of the differences . But if a greater degree of accuracy be insisted on , and you would have a table carried on to 7 or 8 places ...
Página 37
... 12th cases are ambiguous ; since it cannot be determined , by the data , whether AB , C , and AC be greater or less than 90 degrees each . In every right - angled spherical triangle there are five SPHERICAL TRIGONOMETRY . 37.
... 12th cases are ambiguous ; since it cannot be determined , by the data , whether AB , C , and AC be greater or less than 90 degrees each . In every right - angled spherical triangle there are five SPHERICAL TRIGONOMETRY . 37.
Página 41
... less than AC ; since it cannot be determined from the data whether B be acute or obtuse . Two sides AC , The included Upon AB produced ( if need be ) let fall angle ACB the perpendicular CD ; then ( by Theor . BC , and an an gle A ...
... less than AC ; since it cannot be determined from the data whether B be acute or obtuse . Two sides AC , The included Upon AB produced ( if need be ) let fall angle ACB the perpendicular CD ; then ( by Theor . BC , and an an gle A ...
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Términos y frases comunes
ABDP AC by Theor adjacent angle arch bisecting chord circle passing co-sine AC co-tangent of half common logarithm common section Comp describe the circle E. D. COROLLARY E. D. PROP equal to half extremes gent given angle given circle given point half the difference half the sum half the vertical Hence hyperbolic logarithm hypothenuse inclination intersect leg BC line of measures original circle parallel perpendicular plane of projection plane triangle ABC primitive PROB produced projected circle projected pole projecting point radius rectangle right line right-angled spherical triangle SCHOLIUM secant semi-tangents sides similar triangles sine 59 sine AC sine of half sphere spherical angle SPHERICAL PROJECTIONS spherical triangle ABC sum or difference tangent of half THEOREM THOMAS SIMPSON triangle ABC fig versed sine vertical angle whence
Pasajes populares
Página 69 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 79 - ... projection is that of a meridian, or one parallel thereto, and the point of sight is assumed at an infinite distance on a line normal to the plane of projection and passing through the center of the sphere. A circle which is parallel to the plane of projection is projected into an equal circle, a circle perpendicular to the plane of projection is projected into a right line equal in length to the diameter of the projected circle; a circle in any other position is projected into an ellipse, whose...
Página 25 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...
Página 28 - The rectangle of the radius, and sine of the middle part, is equal to the rectangle of the tangents of the two EXTREMES CONJUNCT, and to that of the cosines of the two EXTREMES DISJUNCT.
Página 7 - 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...
Página 28 - In a right angled spherical triangle, the rectangle under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts ; or', to the rectangle under the cosines of the opposite parts.