Mathematics: Compiled from the Best Authors and Intended to be the Text-book of the Course of Private Lectures on These Sciences in the University at Cambridge, Band 2Printed at the University Press, by WilliamHilliard, 1801 |
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Seite 20
... tang . 2 4C - 4B To tang . 2 71 ° 20 ′ 10 * 4712979 44 16 9'9888903 Their sum 115 36 ZC Their diff . 27 04 B Then , As sine 4C115 ° 36 ′ or 64 ° 24 ′ 9'9551259 To sine ZA 37 20 9 * 7827958 So side AB 345 2 * 5378191 To side BC 232 2 ...
... tang . 2 4C - 4B To tang . 2 71 ° 20 ′ 10 * 4712979 44 16 9'9888903 Their sum 115 36 ZC Their diff . 27 04 B Then , As sine 4C115 ° 36 ′ or 64 ° 24 ′ 9'9551259 To sine ZA 37 20 9 * 7827958 So side AB 345 2 * 5378191 To side BC 232 2 ...
Seite 26
... tang . of angle A To the opposite leg BC : :: And so is secant of the ZA : To the hypotenuse AC . * EXAMPLE . D Given In the plane triangle ABC , right - angled at B , AB 162 { 2 ZA 53 ° 07 ' 48 " Required AC and BC . Geometrically ...
... tang . of angle A To the opposite leg BC : :: And so is secant of the ZA : To the hypotenuse AC . * EXAMPLE . D Given In the plane triangle ABC , right - angled at B , AB 162 { 2 ZA 53 ° 07 ' 48 " Required AC and BC . Geometrically ...
Seite 27
... tang . of 53 ° 7 ′ 48 ′′ 10'1249371 : BC 215'9992 2'3344521 And As radius 90 ° 10'0000000 : AB 162 2 * 2095150 :: secant of 53 ° 7 ′ 48 ′′ 10 * 2218477 : AC 269 9993 2'4313627 Instrumentally . The extent from 45 ° to 53 ° 08 ′ , upon ...
... tang . of 53 ° 7 ′ 48 ′′ 10'1249371 : BC 215'9992 2'3344521 And As radius 90 ° 10'0000000 : AB 162 2 * 2095150 :: secant of 53 ° 7 ′ 48 ′′ 10 * 2218477 : AC 269 9993 2'4313627 Instrumentally . The extent from 45 ° to 53 ° 08 ′ , upon ...
Seite 47
... tang . OBP :: BP ( 4 ) : PO = BPX tang . OBP -targ radius OBP ; then OP × BP AOB ; and tang . OBPX number of sides or the area of the polygon . tang . OBP area of the a tabular number , The EXAMPLES . 1. Required the regular pentagon ...
... tang . OBP :: BP ( 4 ) : PO = BPX tang . OBP -targ radius OBP ; then OP × BP AOB ; and tang . OBPX number of sides or the area of the polygon . tang . OBP area of the a tabular number , The EXAMPLES . 1. Required the regular pentagon ...
Seite 175
... tang . BAC 33 ° 98125174 :: 120 feet 2'0791312 : 779289 feet BC 1.8916986 D The distance from the bottom of the tower to the near est tree . Then , As radius 90 ° 10'0000000 : tang . BAD 64 ° 30 ′ 10.3215039 :: BA 120 2 : 0791812 : BD ...
... tang . BAC 33 ° 98125174 :: 120 feet 2'0791312 : 779289 feet BC 1.8916986 D The distance from the bottom of the tower to the near est tree . Then , As radius 90 ° 10'0000000 : tang . BAD 64 ° 30 ′ 10.3215039 :: BA 120 2 : 0791812 : BD ...
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abscisses ADBA altitude angle answer axes axis azimuth base breadth bung diameter cask centre chord circumference cone conjugate cosine course curve declination departure dial diff difference of latitude difference of longitude distance divided draw drawn ecliptic ellipse equal equinoctial EXAMPLES feet figure find the area find the solidity frustum given head diameter height Hence horizon hour angle hour lines hyperbola hypotenuse intersection latit measure meridian middle latitude miles multiply the sum NOTE oblique circle opposite ordinate parabola parallel of latitude parallel sailing parallelogram perpendicular plane sailing pole primitive PROBLEM PROBLEM projection proportion quadrant radius rectangle Required the area Required the content right ascension right line RULE secant segment side sphere spherical triangle spindle square star station stile subtract sun's tance tang tangent THEOREM transverse trapezium triangle ABC ullage wine gallons yards
Beliebte Passagen
Seite 21 - As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.
Seite 17 - To find the other side: — as the sum of the two given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference...
Seite 83 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Seite 328 - The conjugate to any diameter is the line drawn through the centre, and parallel to the tangent of the curve at the vertex of the diameter. So...
Seite 28 - But if the hypothenuse be made radius -, then each leg "will represent the sine of its opposite angle ; namely, the leg AB the sine of the arc AE or angle c, and the leg BC the sine of the arc CD or angle A.
Seite 83 - The axis of a solid is a line drawn from the middle of one end to the middle of the opposite end ; as between the opposite ends of a prism.
Seite 83 - The sphere may be conceived to be formed by the revolution of a semicircle about its diameter, which remains fixed.
Seite 130 - Between these, in a right line, stands an ancient statue, the head whereof is 97 feet from the summit of the higher, and 86 feet from the top of the lower column, and the distance between the...
Seite 205 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 38 - Multiply the sum of the two parallel sides by the perpendicular distance between them, and half the product will be the area.