Trigonometry, Plane and Spherical: With the Construction and Application of Logarithms |
From inside the book
Results 1-5 of 17
Page 6
... Moreover , fince ABC = ABD ( ADB ) + DBC , and C = ADB- DBC ( by 10. 1. ) it is plain that A B C C is = 2 DBC ; or that DBC is equal to Half the Differ- ence of the fame Angles . Now , because of the parallel Lines BF and ED , it will ...
... Moreover , fince ABC = ABD ( ADB ) + DBC , and C = ADB- DBC ( by 10. 1. ) it is plain that A B C C is = 2 DBC ; or that DBC is equal to Half the Differ- ence of the fame Angles . Now , because of the parallel Lines BF and ED , it will ...
Page 11
... moreover ( 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 ...
... moreover ( 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 ...
Page 12
... Moreover mn , being an arithmetical Mean between the Sines B E , DG of the two Extremes ( 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 ...
... Moreover mn , being an arithmetical Mean between the Sines B E , DG of the two Extremes ( 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 ...
Page 24
... Moreover , let CG be the Sine of the Hypo- thenufe , AK its Tangent , AI the Tangent of the Base , CH the Sine of the Perpendicular , and EF the Sine of the Angle at the Bafe ; and let I , K and G , H be joined . Because CH is ...
... Moreover , let CG be the Sine of the Hypo- thenufe , AK its Tangent , AI the Tangent of the Base , CH the Sine of the Perpendicular , and EF the Sine of the Angle at the Bafe ; and let I , K and G , H be joined . Because CH is ...
Page 25
... moreover , that , in right - angled fpherical Triangles ABC , DBC , having one Leg BC common , the Tangents of the Hypothenuses are to each other , inversely , as the Co - fines of the adjacent Angles . For Rad .: Co - fin . ACB :: Tan ...
... moreover , that , in right - angled fpherical Triangles ABC , DBC , having one Leg BC common , the Tangents of the Hypothenuses are to each other , inversely , as the Co - fines of the adjacent Angles . For Rad .: Co - fin . ACB :: Tan ...
Other editions - View all
Common terms and phrases
AB by Theor ABC-ACB AC by Theor AC-BC adjacent Angle alfo known alſo Arch Baſe becauſe bifecting Cafe Chord Circle Co-f Co-fine AC Co-tangent of half common Logarithm confequently Corol COROLLARY demonftrated Diameter equal to Half Excefs fame fhall fince find the Sine firft firſt fubtracted fuppofed garithms given gles Great-Circles half the Bafe half the Difference Half the Sum half the vertical hyperbolic Logarithm Hypothenufe interfect itſelf laft laſt Leg BC likewife Moreover muſt oppofite Angle pendicular perpendicular plane Triangle ABC Progreffion propofed Radius Rectangle refpectively right-angled Spherical Triangle Right-line Secant ſhall Sides AC Sine 59 Sine BCD Sine of half Spherical Triangle ABC Tang Tangent of Half Terms THEOREM thofe Trigonometry Verfed Sine vertical Angle whence whofe
Popular passages
Page 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.
Page 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.
Page 6 - In every plane triangle, it will be, as the sum of any two sides is to their difference...
Page 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.
Page 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...
Page 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.
Page 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.
Page 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...
Page 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...