Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 |
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Strona 6
... intercepted between the sine and the periphery . Thus AF is the versed sine of AB ; and DF of DB . 8. The co - sine of an arch is the part of the diameter in- tercepted between the centre and sine , and is equal to the sine of the ...
... intercepted between the sine and the periphery . Thus AF is the versed sine of AB ; and DF of DB . 8. The co - sine of an arch is the part of the diameter in- tercepted between the centre and sine , and is equal to the sine of the ...
Strona 27
... intercepted by the two circles ACB , ADB form- ing that angle , and whose pole is the angular point A. For let the diameter AB be the intersection of the great circles ADB and ACB ( see Corol.1 . ) , and let the plane , or great cir ...
... intercepted by the two circles ACB , ADB form- ing that angle , and whose pole is the angular point A. For let the diameter AB be the intersection of the great circles ADB and ACB ( see Corol.1 . ) , and let the plane , or great cir ...
Strona 103
... intercepted be- tween the cutting planes , on the same side of their common section , are equal to each other . Case 1. When the cutting planes pass through the centre of the sphere . Let ABDPLG and ACEP ( fig . 52. ) be the cutting ...
... intercepted be- tween the cutting planes , on the same side of their common section , are equal to each other . Case 1. When the cutting planes pass through the centre of the sphere . Let ABDPLG and ACEP ( fig . 52. ) be the cutting ...
Strona 105
... intercepted between the third plane and each of the others , and the cor- responding arcs of the other similarly intercepted arc , are equal , each to each ; and therefore their sums or differences will be equal . But the sum of those ...
... intercepted between the third plane and each of the others , and the cor- responding arcs of the other similarly intercepted arc , are equal , each to each ; and therefore their sums or differences will be equal . But the sum of those ...
Strona 106
... intercepted arc of that circle will be equal to the intercepted arc of the primitive . COROLLARY III . If from an angular point , two right lines be drawn through the poles of its sides , the intercepted arc of the primitive will be the ...
... intercepted arc of that circle will be equal to the intercepted arc of the primitive . COROLLARY III . If from an angular point , two right lines be drawn through the poles of its sides , the intercepted arc of the primitive will be the ...
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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.