Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 Seiten |
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Seite 6
... complement ; and its difference from 180 ° ( or a semicircle ) its supplement . 5. A chord , or subtense , is a right line drawn from one extremity of an arch to the other : thus the right line BE is the chord , or subtense , of the ...
... complement ; and its difference from 180 ° ( or a semicircle ) its supplement . 5. A chord , or subtense , is a right line drawn from one extremity of an arch to the other : thus the right line BE is the chord , or subtense , of the ...
Seite 7
... complement of that arch . Thus HK and CK are the co - tangent and co - secant of AB . 12. A trigonometrical canon is a table exhibiting the length of the sine , tangent , and secant to every degree and minute of the quadrant , with ...
... complement of that arch . Thus HK and CK are the co - tangent and co - secant of AB . 12. A trigonometrical canon is a table exhibiting the length of the sine , tangent , and secant to every degree and minute of the quadrant , with ...
Seite 12
... AC BC G tang . A ( by Theor . II . ) , whose complement is the angle C. Let the angles be found , by Case 6. and then the hyp . AC , by Case 4 . C The solution of the cases of oblique plane triangles . 12 PLANE TRIGONOMETRY .
... AC BC G tang . A ( by Theor . II . ) , whose complement is the angle C. Let the angles be found , by Case 6. and then the hyp . AC , by Case 4 . C The solution of the cases of oblique plane triangles . 12 PLANE TRIGONOMETRY .
Seite 26
... , and thereby form two spherical triangles ABC and FCE , the latter of the tri- angles so formed is said to be the complement of the former ; and vice versa . COROLLARIES . 1. It is manifest ( from Def . SPHERICAL TRIGONOMETRY. ...
... , and thereby form two spherical triangles ABC and FCE , the latter of the tri- angles so formed is said to be the complement of the former ; and vice versa . COROLLARIES . 1. It is manifest ( from Def . SPHERICAL TRIGONOMETRY. ...
Seite 27
... complement of AC , CF of * Note . Although a spherical angle is , properly , the inclination of two great circles , yet it is commonly expressed by the inclination of their peripheries at the point where they intersect each other . BC ...
... complement of AC , CF of * Note . Although a spherical angle is , properly , the inclination of two great circles , yet it is commonly expressed by the inclination of their peripheries at the point where they intersect each other . 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.