Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsKimber and Conrad, 1810 - 125 σελίδες |
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Σελίδα 6
... produced from thence till it meets a right line passing through the centre and the other extremity . Thus AG is the tangent of the arch AB . 10. The secant of an arch is a right line reaching , with- out the circle , from the centre to ...
... produced from thence till it meets a right line passing through the centre and the other extremity . Thus AG is the tangent of the arch AB . 10. The secant of an arch is a right line reaching , with- out the circle , from the centre to ...
Σελίδα 9
... produce AB and CB to the circumference ; then it is evident that BF is the sum , and BH the difference of the sides ... produced , in D and F ; so that CF may express the sum , and CD the difference of the sides AC and AB : join F , B ...
... produce AB and CB to the circumference ; then it is evident that BF is the sum , and BH the difference of the sides ... produced , in D and F ; so that CF may express the sum , and CD the difference of the sides AC and AB : join F , B ...
Σελίδα 33
... produced in I ; lastly , draw QDK perpendicu- lar to OD , meeting OA , OC , and QI produced in Q , L , and K. Because CD BD , it is manifest that OD is not only per- pendicular to the chord BC , but bisects it in E ; whence , also , EF ...
... produced in I ; lastly , draw QDK perpendicu- lar to OD , meeting OA , OC , and QI produced in Q , L , and K. Because CD BD , it is manifest that OD is not only per- pendicular to the chord BC , but bisects it in E ; whence , also , EF ...
Σελίδα 41
... produced ( if need be ) let fall angle ACB the perpendicular CD ; then ( by Theor . 5. ) rad . co - sine AC tang . A co- tang . ACD ; but ( by Cor . 2. to Theor . 1. ) as tang BC : tang . AC :: co - sine ACD : co sine BCD . Whence ACB ...
... produced ( if need be ) let fall angle ACB the perpendicular CD ; then ( by Theor . 5. ) rad . co - sine AC tang . A co- tang . ACD ; but ( by Cor . 2. to Theor . 1. ) as tang BC : tang . AC :: co - sine ACD : co sine BCD . Whence ACB ...
Σελίδα 65
... produced take CD = BC , and let BD be drawn : then ( by Theor . 5. p . 9. ) it will be , AD + AB : AD — AB :: tang . ABD + D 2 A ( 180 ° = 90 ° -A ) : tang 2 ABC ) , that is , AC + BC 2 : ABD D / ABD CBD 2 ― - 2 = + AB : AC + BC - AB ...
... produced take CD = BC , and let BD be drawn : then ( by Theor . 5. p . 9. ) it will be , AD + AB : AD — AB :: tang . ABD + D 2 A ( 180 ° = 90 ° -A ) : tang 2 ABC ) , that is , AC + BC 2 : ABD D / ABD CBD 2 ― - 2 = + AB : AC + BC - AB ...
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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.