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, Volumen2Printed at the University Press, by WilliamHilliard, 1801 |
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Página 12
... side . NOTE . For the sides of triangles the line of numbers , marked Num . is used ; and for the angles , the line of sines , or of tangents , marked Sin . or Tan . according as the proportion respects sines or tangents . If the extent ...
... side . NOTE . For the sides of triangles the line of numbers , marked Num . is used ; and for the angles , the line of sines , or of tangents , marked Sin . or Tan . according as the proportion respects sines or tangents . If the extent ...
Página 13
... side shall be two of them ; to find the rest . In any plane triangle , the sides are proportional to the sines of their opposite angles . * That is , As one side Is to another side So is sin . angle opp . the former To sin . angle opp ...
... side shall be two of them ; to find the rest . In any plane triangle , the sides are proportional to the sines of their opposite angles . * That is , As one side Is to another side So is sin . angle opp . the former To sin . angle opp ...
Página 15
... side AC , measured by the scale of equal parts , will be found to be as follows : viz . ZB 27 ° ZC 115 Or 78 Or 64 AC 174 Or 374 Arithmetically . As side BC 232 2 ° 3654880 To side BA 345 2'5378191 So sine LA37 ° 20 ′ 9'7827958 To sine ...
... side AC , measured by the scale of equal parts , will be found to be as follows : viz . ZB 27 ° ZC 115 Or 78 Or 64 AC 174 Or 374 Arithmetically . As side BC 232 2 ° 3654880 To side BA 345 2'5378191 So sine LA37 ° 20 ′ 9'7827958 To sine ...
Página 17
... sides and the angle included by them ; to find the rest . In a plane triangle , As the sum of any two sides Is to their difference :: So is the tangent of half the sum of their opposite angles : To the tangent of half their difference ...
... sides and the angle included by them ; to find the rest . In a plane triangle , As the sum of any two sides Is to their difference :: So is the tangent of half the sum of their opposite angles : To the tangent of half their difference ...
Página 19
... side will be found by extracting the square root of the sum of the squares of the other two sides ; and then the angles will be found by the first problem . NOTE 2. That instead of the tangent of the half sum , we may use the cotangent ...
... side will be found by extracting the square root of the sum of the squares of the other two sides ; and then the angles will be found by the first problem . NOTE 2. That instead of the tangent of the half sum , we may use the cotangent ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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...
Página 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.
Página 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...
Página 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.
Página 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.
Página 83 - The sphere may be conceived to be formed by the revolution of a semicircle about its diameter, which remains fixed.
Página 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...
Página 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.
Página 38 - Multiply the sum of the two parallel sides by the perpendicular distance between them, and half the product will be the area.