Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 páginas |
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Página 12
... radius is to the sine of A , 1AC and the angles so is the hyp . AC to the leg BC ( by Theor . I. ) The hyp . The angles As AC : BC :: radius : sin . 2 AC and one leg BC The hyp . The other 3 AC and one leg AB A ( Theor . I. ) , whose ...
... radius is to the sine of A , 1AC and the angles so is the hyp . AC to the leg BC ( by Theor . I. ) The hyp . The angles As AC : BC :: radius : sin . 2 AC and one leg BC The hyp . The other 3 AC and one leg AB A ( Theor . I. ) , whose ...
Página 15
... radius . 2. That the secant is a third proportional to the co - sine and radius . 3. That the co - tangent is a fourth proportional to the sine , co - sine , and radius . 4. And that the co - secant is a third proportional to the sine and ...
... radius . 2. That the secant is a third proportional to the co - sine and radius . 3. That the co - tangent is a fourth proportional to the sine , co - sine , and radius . 4. And that the co - secant is a third proportional to the sine and ...
Página 16
... radius to the sine of the common difference , so is the co - sine FO of the mean to half the difference of the sines of the two extremes . For let BD be drawn , intersecting the radius OC in m ; also draw mn parallel to CF , meeting AO ...
... radius to the sine of the common difference , so is the co - sine FO of the mean to half the difference of the sines of the two extremes . For let BD be drawn , intersecting the radius OC in m ; also draw mn parallel to CF , meeting AO ...
Página 17
... radius unity ) be multiplied by twice the co- sine of the common difference , and the sine of either extreme be subtracted from the product , the remainder will be the sine of the other extreme . * Note . Om X CF ос taken in a ...
... radius unity ) be multiplied by twice the co- sine of the common difference , and the sine of either extreme be subtracted from the product , the remainder will be the sine of the other extreme . * Note . Om X CF ос taken in a ...
Página 18
... ( radius being unity ) ; therefore , as the chords of very small arches are to each other nearly as the arches themselves ( vid . p . 181 ) , we shall have , as 1 : 380 :: , 00818121,008726624 , the chord of , or half a degree ; whose ...
... ( radius being unity ) ; therefore , as the chords of very small arches are to each other nearly as the arches themselves ( vid . p . 181 ) , we shall have , as 1 : 380 :: , 00818121,008726624 , the chord of , or half a degree ; whose ...
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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.