Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsJ. Nourse, 1748 - 77 σελίδες |
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Σελίδα 17
... the 2d and 3d Rules , the Sines of all the other intermediate Arches are had , by Addition and Subtraction only . See the Operation . I 45 C. , 000290 , 000290 4915 Excefs , 0000000050 , 05233595 Sine 3 of Sines , Tangents and Secants . 17.
... the 2d and 3d Rules , the Sines of all the other intermediate Arches are had , by Addition and Subtraction only . See the Operation . I 45 C. , 000290 , 000290 4915 Excefs , 0000000050 , 05233595 Sine 3 of Sines , Tangents and Secants . 17.
Σελίδα 36
... Subtraction , only , as thefe do by Multiplication and Division : I fhall here , for the Sake of the young Beginner ( for whom this fmall Tract is chiefly intended ) add a few Pages upon this Subject . But , first of all , it will be ...
... Subtraction , only , as thefe do by Multiplication and Division : I fhall here , for the Sake of the young Beginner ( for whom this fmall Tract is chiefly intended ) add a few Pages upon this Subject . But , first of all , it will be ...
Σελίδα 47
... Subtraction , only , ftill feems wanting in the Calculation of Tables . I fhall , therefore , here fubjoin fuch a Method . 1. Let A , B and C denote any three Numbers in arithmetical Progreffion , not less than 10000 each , whereof the ...
... Subtraction , only , ftill feems wanting in the Calculation of Tables . I fhall , therefore , here fubjoin fuch a Method . 1. Let A , B and C denote any three Numbers in arithmetical Progreffion , not less than 10000 each , whereof the ...
Σελίδα 49
... Subtraction of Logarithms , answers to the Multiplication and Di- vifion of the natural Numbers ( fee p . 36 , 37. ) we have Log , BC Log . Sine 35 ° 20 ′ + Log . 17910— Log . Radius . But , by the Tables of artificial , or logarith ...
... Subtraction of Logarithms , answers to the Multiplication and Di- vifion of the natural Numbers ( fee p . 36 , 37. ) we have Log , BC Log . Sine 35 ° 20 ′ + Log . 17910— Log . Radius . But , by the Tables of artificial , or logarith ...
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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...