Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 páginas |
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Página 7
... greater than 90 ° is equal to the sine of another arch AB as much below 90 ° ; and that its co - sine Cƒ , tan- gent Ag , and secant Cg , are also respectively equal to the co - sine , tangent , and secant of its supplement AB ; but ...
... greater than 90 ° is equal to the sine of another arch AB as much below 90 ° ; and that its co - sine Cƒ , tan- gent Ag , and secant Cg , are also respectively equal to the co - sine , tangent , and secant of its supplement AB ; but ...
Página 9
... greater side AC , describe a circle , and produce AB and CB to the circumference ; then it is 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 ...
... greater side AC , describe a circle , and produce AB and CB to the circumference ; then it is 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 ...
Página 11
... greater ( AC ) , so is radius to the tangent of an angle ( AbC , see Theor . 2. ) 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 ...
... greater ( AC ) , so is radius to the tangent of an angle ( AbC , see Theor . 2. ) 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 ...
Página 18
... greater num- ber of decimals be taken ; by which means you will get the 1 * The Elements of Geometry pubk shed by the same author are here re- ferred to . The same conclusion is easily derived from the scholium to Prop . 11 , book 1 ...
... greater num- ber of decimals be taken ; by which means you will get the 1 * The Elements of Geometry pubk shed by the same author are here re- ferred to . The same conclusion is easily derived from the scholium to Prop . 11 , book 1 ...
Página 21
... greater degree of accuracy be insisted on , and you would have a table carried on to 7 or 8 places , each number ( which is sufficient to give the value of an angle to seconds , and even to thirds , in most cases ) , then the opera ...
... greater degree of accuracy be insisted on , and you would have a table carried on to 7 or 8 places , each number ( which is sufficient to give the value of an angle to seconds , and even to thirds , in most cases ) , then the opera ...
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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.