Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 páginas |
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Página 10
... Abc - 45 ° ) : 8 2 ABC + ACB ABC · ACB tang . : tang . Which gives 2 2 the following theorem , for finding the angles opposite to any * See Prop . 1. Cor . 5 . two proposed sides ; the included angle , and the 10 PLANE TRIGONOMETRY .
... Abc - 45 ° ) : 8 2 ABC + ACB ABC · ACB tang . : tang . Which gives 2 2 the following theorem , for finding the angles opposite to any * See Prop . 1. Cor . 5 . two proposed sides ; the included angle , and the 10 PLANE TRIGONOMETRY .
Página 13
... gives the other an- gle ABC . other Let the angle ABC be found . by the preceding case , and then it will be , sin . C : AB :: sin . ABC : AC ( by Theor . III . ) other As sum of AB and AC : their AC , AB and angles C the included and ...
... gives the other an- gle ABC . other Let the angle ABC be found . by the preceding case , and then it will be , sin . C : AB :: sin . ABC : AC ( by Theor . III . ) other As sum of AB and AC : their AC , AB and angles C the included and ...
Página 19
... of all the in- termediate arches may be had from thence , by barely taking the proportional parts of the differences , and that so near as to give the first six places true in each number OF SINES , TANGENTS , AND SECANTS . 19.
... of all the in- termediate arches may be had from thence , by barely taking the proportional parts of the differences , and that so near as to give the first six places true in each number OF SINES , TANGENTS , AND SECANTS . 19.
Página 20
With the Construction and Application of Logarithms Thomas Simpson. to give the first six places true in each number ; which is sufficiently exact for all common purposes . SCHOLIUM . Although what has been hitherto laid down for ...
With the Construction and Application of Logarithms Thomas Simpson. to give the first six places true in each number ; which is sufficiently exact for all common purposes . SCHOLIUM . Although what has been hitherto laid down for ...
Página 21
... give the value of an angle to seconds , and even to thirds , in most cases ) , then the opera- tion may be as follows : 1o . Multiply the sum of the sines of any two adjacent terms of the progression 45 ' , 1 ° 30 ' , 2 ° 15 ′ , 3 00 ...
... give the value of an angle to seconds , and even to thirds , in most cases ) , then the opera- tion may be as follows : 1o . Multiply the sum of the sines of any two adjacent terms of the progression 45 ' , 1 ° 30 ' , 2 ° 15 ′ , 3 00 ...
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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.