Trigonometry, Plane and Spherical: With the Construction and Application of LogarithmsJ. Nourse, 1748 - 77 Seiten |
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Seite 2
... perpendicular to the Diameter paffing thro ' the other Extremity . Thus BF is the Sine of the Arch AB or DB . 7. The Verfed Sine of an Arch is the Part of the Diameter intercepted between the Sine and the Pe- riphery . Thus AF is the ...
... perpendicular to the Diameter paffing thro ' the other Extremity . Thus BF is the Sine of the Arch AB or DB . 7. The Verfed Sine of an Arch is the Part of the Diameter intercepted between the Sine and the Pe- riphery . Thus AF is the ...
Seite 4
... Perpendicular , fo is the Ra- dius ( of the Table ) to the Sine of the Angle at the Bafe . E 1G For , let AE or AF be the Radius to which the Table of Sines , & c . is adapted , and ED the Sine of the Angle A or Arch EF ( Vid . Def . 3 ...
... Perpendicular , fo is the Ra- dius ( of the Table ) to the Sine of the Angle at the Bafe . E 1G For , let AE or AF be the Radius to which the Table of Sines , & c . is adapted , and ED the Sine of the Angle A or Arch EF ( Vid . Def . 3 ...
Seite 5
... Perpendicular from the Middle of the Bafe . For ( by Cor . to 8 . 2. and the 10. 2. ) , AB + BCXAB - BC AC x 2 DE ; whence AC : AB + BC :: AB - BC : 2DE ( by 3.4 . ) 2 B #A E. D. Α B 3 ED THE- THEOREM V. In any plane Triangle , it will ...
... Perpendicular from the Middle of the Bafe . For ( by Cor . to 8 . 2. and the 10. 2. ) , AB + BCXAB - BC AC x 2 DE ; whence AC : AB + BC :: AB - BC : 2DE ( by 3.4 . ) 2 B #A E. D. Α B 3 ED THE- THEOREM V. In any plane Triangle , it will ...
Seite 10
... Perpendicular BD , and therefore the Angle found by the Proportion , AB ( aB ) : Sin . C :: BC : Sin . A ( or of Ca B , ) may , it is evident , be either the acute Angle A , or the obtufe one C a B ( which is its Supplement ) , the ...
... Perpendicular BD , and therefore the Angle found by the Proportion , AB ( aB ) : Sin . C :: BC : Sin . A ( or of Ca B , ) may , it is evident , be either the acute Angle A , or the obtufe one C a B ( which is its Supplement ) , the ...
Seite 21
... perpendicular to the Plane of the Circle : And the two Points , where the Axis interfects the Surface of the Sphere , are call'd the Poles of the Circle . 3. A fpherical Angle is the Inclination of two Great - Circles . 4. A fpherical ...
... perpendicular to the Plane of the Circle : And the two Points , where the Axis interfects the Surface of the Sphere , are call'd the Poles of the Circle . 3. A fpherical Angle is the Inclination of two Great - Circles . 4. A fpherical ...
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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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 6 - In every plane triangle, it will be, as the sum of any two sides is to their difference...
Seite 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.
Seite 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...
Seite 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.
Seite 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.
Seite 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...
Seite 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...