Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 páginas |
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Página 6
... passing through the other extremity . Thus BF is the sine of the arch AB or DB . 7. The versed sine of an arch is the part of the diameter intercepted between the sine and the periphery . Thus AF is the versed sine of AB ; and DF of DB ...
... passing through the other extremity . Thus BF is the sine of the arch AB or DB . 7. The versed sine of an arch is the part of the diameter intercepted between the sine and the periphery . Thus AF is the versed sine of AB ; and DF of DB ...
Página 26
... passing through the centre . 2. The axis of a circle is a right line passing through the centre of the sphere , perpendicular to the plane of the circle and the two points , where the axis intersects the sur- face of the sphere , are ...
... passing through the centre . 2. The axis of a circle is a right line passing through the centre of the sphere , perpendicular to the plane of the circle and the two points , where the axis intersects the sur- face of the sphere , are ...
Página 27
... passes through the centre ) will be a diame- ter of the sphere ; and consequently , that their peripheries will ... passing through the pole of a given circle , cut that circle at right angles ; because they pass through or coincide ...
... passes through the centre ) will be a diame- ter of the sphere ; and consequently , that their peripheries will ... passing through the pole of a given circle , cut that circle at right angles ; because they pass through or coincide ...
Página 87
... passes through the centre of the sphere ; and the eye is sup- posed to be so situated , that all lines drawn to it from any points on the sphere , are perpendicular to the plane of pro- jection . 3. In the stereographic projection , the ...
... passes through the centre of the sphere ; and the eye is sup- posed to be so situated , that all lines drawn to it from any points on the sphere , are perpendicular to the plane of pro- jection . 3. In the stereographic projection , the ...
Página 90
... passes through the projecting point ( 2. and 4. def . ) , and every radius of the circle is projected into a line equal to it- self ( Cor . 1. › rop . 1. ) 2. E. D. COROLLARY . The radius of the projected circle is the co - sine of the ...
... passes through the projecting point ( 2. and 4. def . ) , and every radius of the circle is projected into a line equal to it- self ( Cor . 1. › rop . 1. ) 2. E. D. COROLLARY . The radius of the projected circle is the co - sine of the ...
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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.