Trigonometry, Plane and Spherical: With the Construction and Application of Logarithms |
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Side 63
F KD E В Let HG , perpendicular G to AB , be the Diameter of a Circle described
about the Triangle , and let HD and Hd be perpendicular to the two Sides of the
Triangle ; A also let CF be parallel to A B , and let HA , HB н and HC be drawn .
F KD E В Let HG , perpendicular G to AB , be the Diameter of a Circle described
about the Triangle , and let HD and Hd be perpendicular to the two Sides of the
Triangle ; A also let CF be parallel to A B , and let HA , HB н and HC be drawn .
Side 64
With the Construction and Application of Logarithms Thomas Simpson. 1 Let the
preceding Figure and Construction be retained , and let AG and CG be drawn .
The Triangles AH D and GHC ( being right - angled at D and C , and having HAD
...
With the Construction and Application of Logarithms Thomas Simpson. 1 Let the
preceding Figure and Construction be retained , and let AG and CG be drawn .
The Triangles AH D and GHC ( being right - angled at D and C , and having HAD
...
Side 65
... and AC , B perpendicular to AB , equal E to a ; about the latter of which , as a
Diameter , let a Circle be described , and , A thro ' O , the Center thereof , let BD
be drawn , meeting the Periphery in E and D ; D also let A , E and C , E be joined
...
... and AC , B perpendicular to AB , equal E to a ; about the latter of which , as a
Diameter , let a Circle be described , and , A thro ' O , the Center thereof , let BD
be drawn , meeting the Periphery in E and D ; D also let A , E and C , E be joined
...
Side 66
... be drawn , and likewise DF , perpendicular to the Base AB , which will , also ,
bisect it , because ( BCD being = ACD ) the Subtenses BD and AD are equal ( by
10. 3. ) Moreover , since the Angle DBE = ACD ( by Cor . to 9.3 . ) = DCB , the ...
... be drawn , and likewise DF , perpendicular to the Base AB , which will , also ,
bisect it , because ( BCD being = ACD ) the Subtenses BD and AD are equal ( by
10. 3. ) Moreover , since the Angle DBE = ACD ( by Cor . to 9.3 . ) = DCB , the ...
Side 67
... be drawn , and I A B also FI , parallel to BD , meeting BA , produced , in I. It is
manifest , from Prop . 13. that CG is equal to Half the Sum of the Sides AC and
BC : It also appears , from 8. 1. and Cor . to 9. 3. that the Triangles DCG , ADE ,
BDE ...
... be drawn , and I A B also FI , parallel to BD , meeting BA , produced , in I. It is
manifest , from Prop . 13. that CG is equal to Half the Sum of the Sides AC and
BC : It also appears , from 8. 1. and Cor . to 9. 3. that the Triangles DCG , ADE ,
BDE ...
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Vanlige uttrykk og setninger
added alſo appears Arch Bafe balf Baſe becauſe Caſe Center Chord Circle Co-f Co-fine Co-ſine AC Co-tang common conſequently COROLLARY Demonſtration determine Diameter Difference drawn equal equal to Half evident Exceſs Extremes fame firſt follows Form gent given gives gles greater half the Difference Half the Sum Hence hyperbolic Logarithm Hypothenuſe Index laſt Logarithm manifeſt meeting Method Minute Moreover Note Number oppoſite parallel perpendicular plane Triangle ABC preceding Product Progreſſion PROP Proportion propoſed Radius Rectangle Remainder reſpectively right-angled ſame Secant ſecond ſee Series ſhall Sides ſince Sine Sine ACD Solution ſuppoſed Table Tang Tangent of Half Tbeor Terms Theor THEOREM thereof theſe thoſe Unity Value verſed Sine vertical Angle whence whoſe
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...
Bibliografisk informasjon
| Tittel | Trigonometry, Plane and Spherical: With the Construction and Application of Logarithms |
| Forfatter | Thomas Simpson |
| Utgiver | J. Nourse, 1748 |
| Original fra | Ghent-universitetet |
| Digitalisert | 17. jan 2008 |
| Lengde | 77 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |