Trigonometry: Plane and Spherical; with the Construction and Application of Logarithms. By Thomas Simpson, F.R.S.F. Wingrave, successor to Mr. Nourse, 1799 - 79 sider |
Inni boken
Resultat 1-5 av 28
Side 6
... because of the fimi- lar triangles ACB and AED , it will be AC : BC :: AE : ED ( by 14.4 . ) 2. E. D .... Thus , if AC , 75 , and BC , 45 ; then it will be , 75,45 ( radius ) : the fine of A6 ; which , in the table , anfwers to 36 ° 52 ...
... because of the fimi- lar triangles ACB and AED , it will be AC : BC :: AE : ED ( by 14.4 . ) 2. E. D .... Thus , if AC , 75 , and BC , 45 ; then it will be , 75,45 ( radius ) : the fine of A6 ; which , in the table , anfwers to 36 ° 52 ...
Side 8
... because of the parallel lines BF and ED , it will be CF : CD :: BF : DE , but BF and DE , because DBF and BDE are right - angles ( by 13.3 . and 7. 1. ) will be tangents of the forefaid angles FDB ( ADB ) and DBE ( DBC ) to the radius ...
... because of the parallel lines BF and ED , it will be CF : CD :: BF : DE , but BF and DE , because DBF and BDE are right - angles ( by 13.3 . and 7. 1. ) will be tangents of the forefaid angles FDB ( ADB ) and DBE ( DBC ) to the radius ...
Side 12
... CH its co - fecant . CE Then ( by 8. 2. ) we have CF the fquare root of EF ; whence , not only the co - fine CF , but alfo the verfed fine AF , ― will 1 will be known . Then because of the fimilar triangles 12 Conftruction of the Table.
... CH its co - fecant . CE Then ( by 8. 2. ) we have CF the fquare root of EF ; whence , not only the co - fine CF , but alfo the verfed fine AF , ― will 1 will be known . Then because of the fimilar triangles 12 Conftruction of the Table.
Side 13
... because of the fimilar triangles CFE , CAT , and CDH , it will be ( by 14. 4. ) 1. CF FE :: CA : CT ; whence the tangent is known . 2. CF : CE ( CA ) :: CA : CT ; whence the fecant is known . 3. EF CF : CD : DH ; whence the co - tan ...
... because of the fimilar triangles CFE , CAT , and CDH , it will be ( by 14. 4. ) 1. CF FE :: CA : CT ; whence the tangent is known . 2. CF : CE ( CA ) :: CA : CT ; whence the fecant is known . 3. EF CF : CD : DH ; whence the co - tan ...
Side 14
... ( because Bm Dm ) is there- fore equal to half their fum , and Dv equal to half their difference . But , because of the fimilar triangles OCF , Omn and Dvm , It will be OC : Om :: CF : mn OC Dm :: FO : Dv } Q. E. D. } 2 COROL- COROLLARYI ...
... ( because Bm Dm ) is there- fore equal to half their fum , and Dv equal to half their difference . But , because of the fimilar triangles OCF , Omn and Dvm , It will be OC : Om :: CF : mn OC Dm :: FO : Dv } Q. E. D. } 2 COROL- COROLLARYI ...
Vanlige uttrykk og setninger
5th rem AB by Theor AC by Theor AC-BC AC+BC adjacent angle alfo alfo known alfo let alſo arch bafe baſe becauſe bifecting cafe chord circle co-f co-fecant co-fine AC co-tangent of half common logarithm confequently COROL COROLLARY diameter dius equal to half excefs fame fecant fecond feries fhall fides AC fince fines firft firſt fpherical triangle ABC fquare fubtracted fupplement fuppofed garithms gles great-circles half the difference half the fum half the vertical Hence hyperbolic logarithm hypothenufe interfect laft leffer leg BC likewife LUKE HANSARD moreover oppofite angle pendicular perpendicular plane triangle ABC progreffion PROP propofed proportion radius reafon refpectively right-angled spherical triangle right-line ſhall ſphere tang tangent of half THEOREM theſe thofe Trigonometry verfed vertical angle whence whofe