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 5
... parallel to it let AT be drawn T and limited by CT : let GB and EM be drawn parallel to AA ' , B ' E ' the latter being limited by CT or CT produced . Then BE is the complement of BA , and angle BCE the comple- ment of angle BCA ; BEA ...
... parallel to it let AT be drawn T and limited by CT : let GB and EM be drawn parallel to AA ' , B ' E ' the latter being limited by CT or CT produced . Then BE is the complement of BA , and angle BCE the comple- ment of angle BCA ; BEA ...
Página 10
... arc , till the prolongation rs becomes equal to cr the secant , and join cs , intersecting the quadrantal arc AE in D. Then , because TSTC , angle tcs Tec TCE , by reason of the parallels TS , CE . Hence BD DE = 10 Plane Trigonometry .
... arc , till the prolongation rs becomes equal to cr the secant , and join cs , intersecting the quadrantal arc AE in D. Then , because TSTC , angle tcs Tec TCE , by reason of the parallels TS , CE . Hence BD DE = 10 Plane Trigonometry .
Página 11
... parallels TS , CE . Hence BD DE = comp . AB , and AS = tan AB + Sec AB = tan AD = tan ( AB + 3 comp AB ) . 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 ...
... parallels TS , CE . Hence BD DE = comp . AB , and AS = tan AB + Sec AB = tan AD = tan ( AB + 3 comp AB ) . 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 ...
Página 14
... parallel to BS , or perpendicular to the radius CB . B H R A R T Then , because of the similar triangles TAC , THR , we shall have , TC : CA :: TR : RH , whence TC . RH = CA. TR , TC : TA :: TR : TH , whence TC . TH = TA . TR . Each of ...
... parallel to BS , or perpendicular to the radius CB . B H R A R T Then , because of the similar triangles TAC , THR , we shall have , TC : CA :: TR : RH , whence TC . RH = CA. TR , TC : TA :: TR : TH , whence TC . TH = TA . TR . Each of ...
Página 15
... parallel - D B N G K L M - BG BCD to DE . Then , it is evident that NE KE + BG , is the sum of the sines of AE and ... parallels DE , LM , we have EN : DN :: bм : bL ; which is evidently the theorem enun- ciated above . - Cor . The sum ...
... parallel - D B N G K L M - BG BCD to DE . Then , it is evident that NE KE + BG , is the sum of the sines of AE and ... parallels DE , LM , we have EN : DN :: bм : bL ; which is evidently the theorem enun- ciated above . - Cor . The sum ...
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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