Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 |
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Strona 9
... evident that BF is the sum , and BH the difference of the sides ; also , since AB + BG = 2AD ( 3. 3. ) = 2AE + 2ED = AB + 2ED ; BG = 2ED . Join AF , HG ; then the angle AFB = BGH ; FAB = BHG ( 21. 3. ) , and ABF = HBG ; therefore AB ...
... evident that BF is the sum , and BH the difference of the sides ; also , since AB + BG = 2AD ( 3. 3. ) = 2AE + 2ED = AB + 2ED ; BG = 2ED . Join AF , HG ; then the angle AFB = BGH ; FAB = BHG ( 21. 3. ) , and ABF = HBG ; therefore AB ...
Strona 14
... evident , be either the acute angle A , or the obtuse one CaB , which is its supplement , the sines of both being ex- actly the same . Having laid down the method of resolving the different cases of plane triangles , by a table of signs ...
... evident , be either the acute angle A , or the obtuse one CaB , which is its supplement , the sines of both being ex- actly the same . Having laid down the method of resolving the different cases of plane triangles , by a table of signs ...
Strona 28
... evident , that the plane GHC will be perpendicu- lar to the plane of the base , and likewise perpendicular to the diameter AL , because GC , being the sine of AC , is perpen- dicular to AL . Moreover , since both the planes OIK and AIK ...
... evident , that the plane GHC will be perpendicu- lar to the plane of the base , and likewise perpendicular to the diameter AL , because GC , being the sine of AC , is perpen- dicular to AL . Moreover , since both the planes OIK and AIK ...
Strona 44
... evident , that what has been above specified , in relation to the properties of the indices of powers , is equally true in the logarithms of numbers ; since logarithms are nothing more than the indices of such powers as agree in value ...
... evident , that what has been above specified , in relation to the properties of the indices of powers , is equally true in the logarithms of numbers ; since logarithms are nothing more than the indices of such powers as agree in value ...
Strona 45
... evident that what has been hitherto said , in respect to the properties of indices , holds equally true in relation to any equimultiples , or like parts , of them ; which have , manifestly , the same properties and proportions , with ...
... evident that what has been hitherto said , in respect to the properties of indices , holds equally true in relation to any equimultiples , or like parts , of them ; which have , manifestly , the same properties and proportions , with ...
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Kluczowe wyrazy i wyrażenia
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
Popularne fragmenty
Strona 69 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Strona 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...
Strona 25 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...
Strona 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.
Strona 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...
Strona 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.