Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 |
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Strona 88
... point in which the eye is supposed to be situated is called the project- ing ... projecting point , is called a projecting line . 7. A circle of the sphere ... projected upon a plane parallel 88 SPHERICAL PROJECTIONS .
... point in which the eye is supposed to be situated is called the project- ing ... projecting point , is called a projecting line . 7. A circle of the sphere ... projected upon a plane parallel 88 SPHERICAL PROJECTIONS .
Strona 89
... projecting lines drawn through all the points of the circle fall in the common section of the planes of the circle and of projection , which is a right line ( 3. 2. Supp . ) , and M that line is equal to the diameter of the circle ...
... projecting lines drawn through all the points of the circle fall in the common section of the planes of the circle and of projection , which is a right line ( 3. 2. Supp . ) , and M that line is equal to the diameter of the circle ...
Strona 90
... 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 distance of its ...
... 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 distance of its ...
Strona 93
... Projection of the Sphere . PROP . I. Any circle passing through the projecting point , is pro- jected into a right line . For lines drawn from the projecting point to any part of the circle will be in its plane ; and will therefore meet ...
... Projection of the Sphere . PROP . I. Any circle passing through the projecting point , is pro- jected into a right line . For lines drawn from the projecting point to any part of the circle will be in its plane ; and will therefore meet ...
Strona 94
... projecting point is pro- jected into a right line perpendicular to the line of measures , and distant from the centre the semi - tangent of its nearest distance from the pole opposite to the projecting point . Thus if AE be a circle ...
... projecting point is pro- jected into a right line perpendicular to the line of measures , and distant from the centre the semi - tangent of its nearest distance from the pole opposite to the projecting point . Thus if AE be a circle ...
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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
Popularne fragmenty
Strona 69 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Strona 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...
Strona 25 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...
Strona 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.
Strona 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...
Strona 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.