Elements of Plane and Spherical Trigonometry: With Their Applications to Heights and Distances Projections of the Sphere, Dialling, Astronomy, the Solution of Equations, and Geodesic OperationsBaldwin, Cradock, and Joy, 1816 - 244 páginas |
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Página 6
... evident from the consideration that a right line AB is less than any curve line terminated by the same points , and the perpendicular BD less than the hypothenuse AB , of a right angled triangle ADB . ( B ) . The sine BD of an arc AB ...
... evident from the consideration that a right line AB is less than any curve line terminated by the same points , and the perpendicular BD less than the hypothenuse AB , of a right angled triangle ADB . ( B ) . The sine BD of an arc AB ...
Página 11
... evident that the sine of 30 ° , tangent of 45 ° , and secant of 60 ° , are in the ratio of the numbers 1 , 2 , and 4 ; or that tan 45 ° is a mean proportional between sin 30 ° and sec 60o . PROP . VII ... 7. The square of the sine ...
... evident that the sine of 30 ° , tangent of 45 ° , and secant of 60 ° , are in the ratio of the numbers 1 , 2 , and 4 ; or that tan 45 ° is a mean proportional between sin 30 ° and sec 60o . PROP . VII ... 7. The square of the sine ...
Página 14
... evident by a suitable modification of the diagram ; and will still farther ap- pear in the fourth chapter of this work . PROP . X. 10. As the difference or sum of the square of the radius and the rectangle under the tangents of two arcs ...
... evident by a suitable modification of the diagram ; and will still farther ap- pear in the fourth chapter of this work . PROP . X. 10. As the difference or sum of the square of the radius and the rectangle under the tangents of two arcs ...
Página 15
... evident that NE KE + BG , is the sum of the sines of AE and AB , and ND = KE KD KN , is their difference . Also , since BIE ( at the circumference ) BCE ( at the centre ) ; and BID = ( Euc . iii . 20 ) ; bм is equal to the tangent of ...
... evident that NE KE + BG , is the sum of the sines of AE and AB , and ND = KE KD KN , is their difference . Also , since BIE ( at the circumference ) BCE ( at the centre ) ; and BID = ( Euc . iii . 20 ) ; bм is equal to the tangent of ...
Página 20
... evident , since K IA = AD , and CA perpendicular to BD , that CI CD , ICA DCA , and there- fore BCI BCA ACD : also that ed is the sine of the sum of the given angles , and ik the sine of their differ- e ce , to the assumed radius Ac ...
... evident , since K IA = AD , and CA perpendicular to BD , that CI CD , ICA DCA , and there- fore BCI BCA ACD : also that ed is the sine of the sum of the given angles , and ik the sine of their differ- e ce , to the assumed radius Ac ...
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Términos y frases comunes
altitude angled spherical triangle azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine cotangent declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulæ given side h cos h half Hence horizon hour angle hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian obliq oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius right angled spherical right angled triangle right ascension right line sec² secant sin A sin sin² sine solid angle sphere spherical excess spherical trigonometry star substyle sun's supposed surface tan² tangent theorem three angles three sides tion triangle ABC values versed sine versin vertical angle whence zenith