Trigonometry, Plane and Spherical: With the Construction and Application of Logarithms |
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Página 11
And as radius to the tangent of the excess of this angle above 45 ° , so is the
tangent of half the sum of the required angles to the tangent of half their
difference * . * This theorem , though it requires two proportions , is commonly
used by ...
And as radius to the tangent of the excess of this angle above 45 ° , so is the
tangent of half the sum of the required angles to the tangent of half their
difference * . * This theorem , though it requires two proportions , is commonly
used by ...
Página 18
The sine of any arch , above 60 degrees , is equal to the sine of another arch , as
much below 60 ° , together with the sine of its excess above 60 ° . PROP . III . To
find the sine of a very small arch ; suppose that of ; 15 ' . 1 It is found , in p .
The sine of any arch , above 60 degrees , is equal to the sine of another arch , as
much below 60 ° , together with the sine of its excess above 60 ° . PROP . III . To
find the sine of a very small arch ; suppose that of ; 15 ' . 1 It is found , in p .
Página 21
Note . The co - sine of the difference of two arches ( supposing radius unity ) is
found by adding the product of their sines to that of their co - sinesi as is hereafter
demonstrated , 20. From this excess let the first product be continually OF SINES
...
Note . The co - sine of the difference of two arches ( supposing radius unity ) is
found by adding the product of their sines to that of their co - sinesi as is hereafter
demonstrated , 20. From this excess let the first product be continually OF SINES
...
Página 22
From this excess let the first product be continually subtracted ; that is , first , from
the excess itself ; then from the remainder ; then from the last remainder , and so
on 44 - times . 3 ° . To the lesser extreme add the forementioned excess ; and to ...
From this excess let the first product be continually subtracted ; that is , first , from
the excess itself ; then from the remainder ; then from the last remainder , and so
on 44 - times . 3 ° . To the lesser extreme add the forementioned excess ; and to ...
Página 23
sine 3 ° 0 , 000290 4915 excess , 0000000050 , 05233595 , 0002904915 4865 1
st . rem . 50 , 0526264415 sine 3 ° 1 ' 2904865 4815 2d . rem . 50 , 0529169280
sine 3 ° 2 ' 2904815 14765 3d . rem . 50 , 0532074095 sine 3 ° 3 ' 2904765 ...
sine 3 ° 0 , 000290 4915 excess , 0000000050 , 05233595 , 0002904915 4865 1
st . rem . 50 , 0526264415 sine 3 ° 1 ' 2904865 4815 2d . rem . 50 , 0529169280
sine 3 ° 2 ' 2904815 14765 3d . rem . 50 , 0532074095 sine 3 ° 3 ' 2904765 ...
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Términos y frases comunes
added arch base called centre circle co-s co-sine AC co-tang common Comp complement consequently COROLLARY describe the circle diameter difference distance draw drawn equal evident excess extremes follows given angle given point gives greater half the difference half the sum Hence hypothenuse inclination intercepted intersect join known less line of measures logarithm manifest meeting minute Moreover oblique opposite parallel passing perpendicular plane of projection pole primitive PROB produced projecting point PROP proportion proposed proposition radius rectangle respectively right angles right line RULE secant semi-tangents sides similar sine sine AC sphere supposed tang tangent of half Theor THEOREM triangle ABC fig Trigonometry 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.
Información bibliográfica
| Título | Trigonometry, Plane and Spherical: With the Construction and Application of Logarithms |
| Autor | Thomas Simpson |
| Editor | Kimber and Conrad, 1810 |
| Procedencia del original | Biblioteca Pública de Nueva York |
| Digitalizado | 22 Jun. 2006 |
| Largo | 125 páginas |
| Exportar cita | BiBTeX EndNote RefMan |