Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 Seiten |
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Seite 7
... hypothenuse is to the perpendicular , so is the radius ( of the table ) to the sine of the angle at the base . For , let AE or AF be the radius to which the table of sines , & c . is adapted , and ED the sine of the angle A or arch EF ...
... hypothenuse is to the perpendicular , so is the radius ( of the table ) to the sine of the angle at the base . For , let AE or AF be the radius to which the table of sines , & c . is adapted , and ED the sine of the angle A or arch EF ...
Seite 28
... hypothenuse to the tangent of the base . DEMONSTRATION . Let ADL and AEL ( fig . 13. ) be two great circles of the ... hypothenuse , and BAC ( ar DAE = DE DOE ) the angle at the base : moreover , let CG be the sine of the hypothenuse ...
... hypothenuse to the tangent of the base . DEMONSTRATION . Let ADL and AEL ( fig . 13. ) be two great circles of the ... hypothenuse , and BAC ( ar DAE = DE DOE ) the angle at the base : moreover , let CG be the sine of the hypothenuse ...
Seite 29
... hypothenuses are to each other , inversely , as the co - sines of the adjacent angles . For radius co - sine ACB : : tan . AC : tan . BC 2 sinceradius : co - sine DCB :: tan . DC : tan . BC S by the latter part of the theorem ; we shall ...
... hypothenuses are to each other , inversely , as the co - sines of the adjacent angles . For radius co - sine ACB : : tan . AC : tan . BC 2 sinceradius : co - sine DCB :: tan . DC : tan . BC S by the latter part of the theorem ; we shall ...
Seite 30
... hypothenuse . DEMONSTRATION . Let CEF be the complemental triangle to ABC , accord- ing to what has been already ... hypothenuses will be to each other , directly , as the co - sines of their bases . For Srad co - sin . BC : : co - sin ...
... hypothenuse . DEMONSTRATION . Let CEF be the complemental triangle to ABC , accord- ing to what has been already ... hypothenuses will be to each other , directly , as the co - sines of their bases . For Srad co - sin . BC : : co - sin ...
Seite 32
... hypothenuse , so is the tangent of either angle to the co - tangent of the other angle . For , CEF ( fig . 11. ) being as in the last , it will be , as ra- dius sine CE :: tang . C : tang . EF ( by Theorem 4. ) ; that is , radius : co ...
... hypothenuse , so is the tangent of either angle to the co - tangent of the other angle . For , CEF ( fig . 11. ) being as in the last , it will be , as ra- dius sine CE :: tang . C : tang . EF ( by Theorem 4. ) ; that is , radius : co ...
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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.