Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 Seiten |
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Seite 6
... produced from thence till it meets a right line passing through the centre and the other extremity . Thus AG is the tangent of the arch AB . 10. The secant of an arch is a right line reaching , with- out the circle , from the centre to ...
... produced from thence till it meets a right line passing through the centre and the other extremity . Thus AG is the tangent of the arch AB . 10. The secant of an arch is a right line reaching , with- out the circle , from the centre to ...
Seite 9
... produce AB and CB to the circumference ; then it is evident that BF is the sum , and BH the difference of the sides ... produced , in D and F ; so that CF may express the sum , and CD the difference of the sides AC and AB : join F , B ...
... produce AB and CB to the circumference ; then it is evident that BF is the sum , and BH the difference of the sides ... produced , in D and F ; so that CF may express the sum , and CD the difference of the sides AC and AB : join F , B ...
Seite 33
... produced in I ; lastly , draw QDK perpendicu- lar to OD , meeting OA , OC , and QI produced in Q , L , and K. B Because CD BD , it is manifest that OD is not only per pendicular to the chord BC , but bisects it in E ; whence , also , EF ...
... produced in I ; lastly , draw QDK perpendicu- lar to OD , meeting OA , OC , and QI produced in Q , L , and K. B Because CD BD , it is manifest that OD is not only per pendicular to the chord BC , but bisects it in E ; whence , also , EF ...
Seite 41
... produced ( if need be ) let fall angle ACB the perpendicular CD ; then ( by Theor . BC , and an an gle A opposite 2 to one of them ) Two sides AC , BC , and an an- gle opposite to Jone of them Two sides AC , AB , and the in- 4cluded ...
... produced ( if need be ) let fall angle ACB the perpendicular CD ; then ( by Theor . BC , and an an gle A opposite 2 to one of them ) Two sides AC , BC , and an an- gle opposite to Jone of them Two sides AC , AB , and the in- 4cluded ...
Seite 65
... produced take CD BC , and let BD be drawn : then ( by Theor . 5. p . 9. ) it will be , AD + AB : AD — AB ABD + D 180 ° A :: tang . - = 90 ° - -- 1A ) : tang . 2 2 ( ABD CBD 2 = ABC ) , ) , that is , AC + BC ABD D / ABD 2 - + AB AC + BC ...
... produced take CD BC , and let BD be drawn : then ( by Theor . 5. p . 9. ) it will be , AD + AB : AD — AB ABD + D 180 ° A :: tang . - = 90 ° - -- 1A ) : tang . 2 2 ( ABD CBD 2 = ABC ) , ) , that is , AC + BC ABD D / ABD 2 - + AB AC + BC ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 69 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Seite 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...
Seite 25 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...
Seite 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.
Seite 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...
Seite 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.