Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsJ. Nourse, 1748 - 77 σελίδες |
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Σελίδα 4
... because of the fi- milar Triangles ACB and AED , it will be AC : BC :: AE : ED ( by 5 . 4. ) 2. E. D. Thus , if AC = , 75 , and BC = , 45 ; then it will be , 75,45 I ( Radius ) : the Sine of A = , 6 ; which , in the Table , answers to ...
... because of the fi- milar Triangles ACB and AED , it will be AC : BC :: AE : ED ( by 5 . 4. ) 2. E. D. Thus , if AC = , 75 , and BC = , 45 ; then it will be , 75,45 I ( Radius ) : the Sine of A = , 6 ; which , in the Table , answers to ...
Σελίδα 6
... 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 11.3 . and 8. 1. ) will be Tangents of the forefaid Angles FDB ( ADB ) and DBE ( DBC ) to the Radius BD ...
... 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 11.3 . and 8. 1. ) will be Tangents of the forefaid Angles FDB ( ADB ) and DBE ( DBC ) to the Radius BD ...
Σελίδα 11
... ( because AT : AC :: CD ( AC ) : DH ) , that the Rectangle of the Tangent and Co - tangent is equal to the Square of the Ra- dius ( by 3.4 . ) : Whence it likewife follows , that the Tangent of Half a Right - angle is equal to the Ra ...
... ( because AT : AC :: CD ( AC ) : DH ) , that the Rectangle of the Tangent and Co - tangent is equal to the Square of the Ra- dius ( by 3.4 . ) : Whence it likewife follows , that the Tangent of Half a Right - angle is equal to the Ra ...
Σελίδα 12
... ( because Bm Dm ) is there- fore equal to Half their Sum , and Dv equal to Half their Difference . But , because of the fimilar Triangles OCF , Omn and Dum , It will be SOC : Om :: CF : mn OC Dm :: FO : Dv } Q. E.D. COROLLARY L Because of ...
... ( because Bm Dm ) is there- fore equal to Half their Sum , and Dv equal to Half their Difference . But , because of the fimilar Triangles OCF , Omn and Dum , It will be SOC : Om :: CF : mn OC Dm :: FO : Dv } Q. E.D. COROLLARY L Because of ...
Σελίδα 13
With the Construction and Application of Logarithms Thomas Simpson. COROLLARY L Because of the foregoing Proportions , we have ' DG + BE mn 2 3 ) = OmxCF and Dv OC ( DG - BE ) Dm xFO 20mxCF ; and therefore DG + BE = OC OC 2Dm × FO and DG ...
With the Construction and Application of Logarithms Thomas Simpson. COROLLARY L Because of the foregoing Proportions , we have ' DG + BE mn 2 3 ) = OmxCF and Dv OC ( DG - BE ) Dm xFO 20mxCF ; and therefore DG + BE = OC OC 2Dm × FO and DG ...
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Δημοφιλή αποσπάσματα
Σελίδα 1 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees; and each degree into 60 minutes, each minute into 60 seconds, and so on.
Σελίδα 3 - 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 6 - In every plane triangle, it will be, as the sum of any two sides is to their difference...
Σελίδα 41 - 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 13 - If the sine of the mean of three equidifferent arcs' dius being unity) be multiplied into twice the cosine of the common difference, and the sine of either extreme be deducted from the product, the remainder will be the sine of the other extreme. (B.) The sine of any arc above 60°, is equal to the sine of another arc as much below 60°, together with the sine of its excess above 60°. Remark. From this latter proposition, the sines below 60° being known, those of arcs above 60° are determinable...
Σελίδα 31 - ... is the tangent of half the vertical angle to the tangent of the angle which the perpendicular CD makes with the line CF, bisecting the vertical angle.
Σελίδα 73 - BD, is to their Difference ; fo is the Tangent of half the Sum of the Angles BDC and BCD, to the Tangent of half their Difference.
Σελίδα 28 - As the sum of the sines of two unequal arches is to their difference, so is the tangent of half the sum of those arches to the tangent of half their difference : and as the sum...
Σελίδα 68 - In any right lined triangle, having two unequal sides ; as the less of those sides is to the greater, so is radius to the tangent of an angle ; and as radius is to the tangent of the excess of...