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 9
... PROP . I. 1. THE chord of any arc is a mean proportional be- tween the versed sine of that arc and the diameter of the circle . * The nature and use of logarithms being fully explained in Dr. Hutton's valuable work , and , indeed , in ...
... PROP . I. 1. THE chord of any arc is a mean proportional be- tween the versed sine of that arc and the diameter of the circle . * The nature and use of logarithms being fully explained in Dr. Hutton's valuable work , and , indeed , in ...
Página 10
... PROP . II . L CD A 2. As radius : cosine of any arc :: twice the sine of that are the sine of double the arc . In the preceding figure CH is the cosine of the arc BN , AB is twice the sine вH of that arc , and BD is the sine of AB the ...
... PROP . II . L CD A 2. As radius : cosine of any arc :: twice the sine of that are the sine of double the arc . In the preceding figure CH is the cosine of the arc BN , AB is twice the sine вH of that arc , and BD is the sine of AB the ...
Página 11
... PROP . V. 5. The chord of 60 ° is equal to the radius of the cir- cle ; the versed sine , and cosine of 60 ° are each equal to half the radius ; and the secant of 60 ° is equal to double the radius . Let AB be an arc of 60 ° , AB its ...
... PROP . V. 5. The chord of 60 ° is equal to the radius of the cir- cle ; the versed sine , and cosine of 60 ° are each equal to half the radius ; and the secant of 60 ° is equal to double the radius . Let AB be an arc of 60 ° , AB its ...
Página 12
... PROP . VII ... 7. The square of the sine of half any arc or angle is equal to a rectangle under half the radius and ... prop . 1 , of this chapter . For 4AH * AB2 AL . AD Whence AH2 = AC . AD . 2AC . AD . Also , 4CH2 = LB2 AL . LD = 2AC ...
... PROP . VII ... 7. The square of the sine of half any arc or angle is equal to a rectangle under half the radius and ... prop . 1 , of this chapter . For 4AH * AB2 AL . AD Whence AH2 = AC . AD . 2AC . AD . Also , 4CH2 = LB2 AL . LD = 2AC ...
Página 13
... prop . 2 of this chapter . PROP . IX . 9. The rectangle under the radius and the cosine of the sum or the difference of two arcs , is equal to the difference or the sum of the rectangles under their res- pective cosines and sines ...
... prop . 2 of this chapter . PROP . IX . 9. The rectangle under the radius and the cosine of the sum or the difference of two arcs , is equal to the difference or the sum of the rectangles under their res- pective cosines and sines ...
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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