Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 σελίδες |
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Σελίδα 18
... semi - periphery is expressed by , 00818121 ( radius being unity ) ... half a degree ; whose half , or , 004363312 , is therefore the sine of 15 ' , very nearly . From whence the sine of ... TANGENTS , AND SECANTS . 18 CONSTRUCTION OF THE TABLE.
... semi - periphery is expressed by , 00818121 ( radius being unity ) ... half a degree ; whose half , or , 004363312 , is therefore the sine of 15 ' , very nearly . From whence the sine of ... TANGENTS , AND SECANTS . 18 CONSTRUCTION OF THE TABLE.
Σελίδα 19
With the Construction and Application of Logarithms Thomas Simpson. chord of OF SINES , TANGENTS , AND SECANTS . 19 part of the semi - periphery to what accuracy you please : then , by proceeding as above ( for finding the sine of 15 ...
With the Construction and Application of Logarithms Thomas Simpson. chord of OF SINES , TANGENTS , AND SECANTS . 19 part of the semi - periphery to what accuracy you please : then , by proceeding as above ( for finding the sine of 15 ...
Σελίδα 69
... tangent of the vertical angle of a plane triangle ABC ( fig . 28. ) is to radius , so is the base AB to a fourth proportional ; and as the said fourth proportional is to the sum of the semi - base and the line CD bisecting the base , so ...
... tangent of the vertical angle of a plane triangle ABC ( fig . 28. ) is to radius , so is the base AB to a fourth proportional ; and as the said fourth proportional is to the sum of the semi - base and the line CD bisecting the base , so ...
Σελίδα 93
... semi - tangent of its dis- tance from the pole opposite to the projecting point . Let E ( fig . 42. ) be the point ... tangent of GM , or the semi - tangent of EM . COROLLARY I. Any circle passing through the projecting point is ...
... semi - tangent of its dis- tance from the pole opposite to the projecting point . Let E ( fig . 42. ) be the point ... tangent of GM , or the semi - tangent of EM . COROLLARY I. Any circle passing through the projecting point is ...
Σελίδα 94
... semi - tangent of its nearest distance from the pole opposite to the projecting point . Thus if AE be a circle passing through A , and at right . angles ... semi - tangents of its greatest and least distances from 94 SPHERICAL PROJECTIONS .
... semi - tangent of its nearest distance from the pole opposite to the projecting point . Thus if AE be a circle passing through A , and at right . angles ... semi - tangents of its greatest and least distances from 94 SPHERICAL PROJECTIONS .
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABDP AC by Theor adjacent angle AE² bisecting chord circle passing co-s 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 inclination intersect leg BC less circle 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 triangle ABC sum or difference tang tangent of half THEOREM triangle ABC fig versed sine vertical angle whence
Δημοφιλή αποσπάσματα
Σελίδα 2 - An Act for the Encouragement of Learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies during the time* therein mentioned," and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints.
Σελίδα 2 - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Σελίδα 9 - Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the Tangent of half the Sum of the two opposite Angles ; To the Tangent of half the Difference between them.
Σελίδα 5 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Σελίδα 7 - Canon, is a table showing the length of the sine, tangent, and secant, to every degree and minute of the quadrant, with respect to the radius, which is expressed by unity or 1, with any number of ciphers.
Σελίδα 32 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Σελίδα 38 - 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.
Σελίδα 89 - ... 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...
Σελίδα 48 - The sum of the logarithms of any two numbers is equal to the logarithm of their product. Therefore, the addition of logarithms corresponds to the multiplication of their numbers.
Σελίδα 38 - 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.