Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsJ. Nourse, 1748 - 77 sider |
Inni boken
Resultat 1-5 av 11
Side 3
... Unity , and conceived to be divided into 10000 , or more , Decimal Parts . By the Help of this Table , and the Doctrine of fimilar Triangles , the whole Bufinefs of Trigonometry is performed ; which I fhall now proceed to fhew . But ...
... Unity , and conceived to be divided into 10000 , or more , Decimal Parts . By the Help of this Table , and the Doctrine of fimilar Triangles , the whole Bufinefs of Trigonometry is performed ; which I fhall now proceed to fhew . But ...
Side 13
... Unity ) be multiplied by twice the Co - fine of the common Difference , and the Sine of either Extreme be fubtracted from the Product , the Remainder will be the Sine of the other Extreme . 2. The Sine of any Arch , above 60 Degrees ...
... Unity ) be multiplied by twice the Co - fine of the common Difference , and the Sine of either Extreme be fubtracted from the Product , the Remainder will be the Sine of the other Extreme . 2. The Sine of any Arch , above 60 Degrees ...
Side 14
... Unity ) ; therefore , as the Chords of very fmall Arches are to each other nearly as the Arches themselves ( vid . p . 140. ) we fhall have , as 34:35 :: , 00818121 : , 008726624 , the Chord of , or Half a Degree ; whofe Half , or ...
... Unity ) ; therefore , as the Chords of very fmall Arches are to each other nearly as the Arches themselves ( vid . p . 140. ) we fhall have , as 34:35 :: , 00818121 : , 008726624 , the Chord of , or Half a Degree ; whofe Half , or ...
Side 16
... 2 Arches ( fuppofing Radius Unity ) , is found by adding the Product of their Sines to that of their Co - fines ; as is hereafter demonftrated . 2o . From 2o . From this Excefs let the firft Product be 16 Conftruction of the Table.
... 2 Arches ( fuppofing Radius Unity ) , is found by adding the Product of their Sines to that of their Co - fines ; as is hereafter demonftrated . 2o . From 2o . From this Excefs let the firft Product be 16 Conftruction of the Table.
Side 36
... Unity , and common Ratio any given Quantity a . Then it is manifeft , 1. That , the Sum of the Indices of any two Terms of the Progreffion is equal to the Index of the Product of thofe Terms . Thus 2 + 3 ( 5 ) is the Index of a2 x a3 ...
... Unity , and common Ratio any given Quantity a . Then it is manifeft , 1. That , the Sum of the Indices of any two Terms of the Progreffion is equal to the Index of the Product of thofe Terms . Thus 2 + 3 ( 5 ) is the Index of a2 x a3 ...
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Trigonometry, Plane and Spherical;: With the Construction and Application of ... Thomas Simpson Uten tilgangsbegrensning - 1765 |
Trigonometry, Plane and Spherical: With the Construction and Application of ... Thomas Simpson Uten tilgangsbegrensning - 1765 |
Trigonometry, Plane and Spherical: With the Construction and Application of ... Thomas Simpson Uten tilgangsbegrensning - 1765 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 6 - In every plane triangle, it will be, as the sum of any two sides is to their difference...
Side 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.
Side 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...
Side 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.
Side 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.
Side 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...
Side 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...