Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 páginas |
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Página 24
... excess , 0000000730 1st . prod . , 85940641 sine 59 ° 15 ' 0001486947 86217 1st . rem . 730 , 8595551047 sine 59 ° 16 ' 1486217 85487 2d . rem . 730 , 8597037264 sine 59 ° 17 ' 1485487 84757 3d . rem . 730 , 8598522751 sine 59 ° 18 ...
... excess , 0000000730 1st . prod . , 85940641 sine 59 ° 15 ' 0001486947 86217 1st . rem . 730 , 8595551047 sine 59 ° 16 ' 1486217 85487 2d . rem . 730 , 8597037264 sine 59 ° 17 ' 1485487 84757 3d . rem . 730 , 8598522751 sine 59 ° 18 ...
Página 44
... excess of a above unity , indefinitely little ; so that some term or other of the progression 1 , a , a2 , a3 , aa , a3 , & c . may be equal to , or coincide with each term of the series of natural numbers , 2 , 3 , 4 , 5 , 6 , 7 , & c ...
... excess of a above unity , indefinitely little ; so that some term or other of the progression 1 , a , a2 , a3 , aa , a3 , & c . may be equal to , or coincide with each term of the series of natural numbers , 2 , 3 , 4 , 5 , 6 , 7 , & c ...
Página 45
... excess of the common ra- tio above unity . Thus , if e be an indefinitely small quantity , the hyperbo- lic logarithm of the natural number agreeing with any term . 1 + e " of the logarithmic progression 1 , 1 + e , 1 + e ] 2 1 + e ] 3 ...
... excess of the common ra- tio above unity . Thus , if e be an indefinitely small quantity , the hyperbo- lic logarithm of the natural number agreeing with any term . 1 + e " of the logarithmic progression 1 , 1 + e , 1 + e ] 2 1 + e ] 3 ...
Página 54
... and C , and let the remainder be di- vided by 10000 . 3. Multiply the quotient by 49,5 , and to the product add part of the difference of the logarithms of A ' and 1 B ; then the sum will be the excess of 54 THE NATURE AND.
... and C , and let the remainder be di- vided by 10000 . 3. Multiply the quotient by 49,5 , and to the product add part of the difference of the logarithms of A ' and 1 B ; then the sum will be the excess of 54 THE NATURE AND.
Página 55
... excess of the logarithm of A +1 above that of A. 4. From this excess let the quotient , found by Rule 2. , be continually subtracted , that is , first from the excess it- self , then from the remainder , then from the next remain- der ...
... excess of the logarithm of A +1 above that of A. 4. From this excess let the quotient , found by Rule 2. , be continually subtracted , that is , first from the excess it- self , then from the remainder , then from the next remain- der ...
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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.