Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsJ. Nourse, 1748 - 77 σελίδες |
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Σελίδα 6
... equal to Half the Sum of the Angles op- pofite to the Sides propos'd . 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 ...
... equal to Half the Sum of the Angles op- pofite to the Sides propos'd . 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 ...
Σελίδα 7
... equal , each to each , it will be ( by Equa- AbC + ACb Abc - ACb A lity ) , as Tang . : Tang . 2 2 Tang . ABC + ACB ... Half the Sum of the required Angles to the Tangent of Half their Difference * . * This Theorem , tho ' it requires ...
... equal , each to each , it will be ( by Equa- AbC + ACb Abc - ACb A lity ) , as Tang . : Tang . 2 2 Tang . ABC + ACB ... Half the Sum of the required Angles to the Tangent of Half their Difference * . * This Theorem , tho ' it requires ...
Σελίδα 11
... 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- dius ; and that the Co - tangents of any two dif- ferent Arches ( represented by P and Q are to ...
... 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- dius ; and that the Co - tangents of any two dif- ferent Arches ( represented by P and Q are to ...
Σελίδα 12
... Half the Sum of the Sines BE + DG , of the two Extremes : And , as Radius to ... equal to each other ( by Hypothefis ) , OC is not only perpen- dicular to ... equal to Half their Sum , and Dv equal to Half their Difference . But , because ...
... Half the Sum of the Sines BE + DG , of the two Extremes : And , as Radius to ... equal to each other ( by Hypothefis ) , OC is not only perpen- dicular to ... equal to Half their Sum , and Dv equal to Half their Difference . But , because ...
Σελίδα 15
... . 138 and 139 of the Elements ) = √2 + √3 = , 965925826 , & c . ( the Supplement Chord of 30 ° ) and the Sine of 18 ° , which is√ = , 309017 , 309017 , & c . ( equal to Half the of Sines , Tangents and Secants . 15.
... . 138 and 139 of the Elements ) = √2 + √3 = , 965925826 , & c . ( the Supplement Chord of 30 ° ) and the Sine of 18 ° , which is√ = , 309017 , 309017 , & c . ( equal to Half the of Sines , Tangents and Secants . 15.
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
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...