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 9
... triangle , or two right angles , is equal to 180 ° . Wherefore , in a right - angled triangle , one acute angle being subtracted from 90 ° , the remainder will be the other ; and the sum of any two angles of a triangle , being taken ...
... triangle , or two right angles , is equal to 180 ° . Wherefore , in a right - angled triangle , one acute angle being subtracted from 90 ° , the remainder will be the other ; and the sum of any two angles of a triangle , being taken ...
Seite 11
... triangles , or the cases of trigonometry ; namely , Geometrical Con- struction , Arithmetical Computation , and Instrumental Op- eration . In the first method ; let the triangle be constructed by making the parts of the given magnitudes ...
... triangles , or the cases of trigonometry ; namely , Geometrical Con- struction , Arithmetical Computation , and Instrumental Op- eration . In the first method ; let the triangle be constructed by making the parts of the given magnitudes ...
Seite 12
... triangle there must be given three parts , one of which , at least , must be a side ; because the same angles are common to an infinite number of triangles . In plane trigonometry , there are only three cases , or va- rieties , viz . 1 ...
... triangle there must be given three parts , one of which , at least , must be a side ; because the same angles are common to an infinite number of triangles . In plane trigonometry , there are only three cases , or va- rieties , viz . 1 ...
Seite 14
... triangle . EXAMPLE I , In the plane triangle ABC , Given { AB 345 yards BC 232 LA 37 ° 20 ′ ; Required the other parts . Geometrically . 1. Draw the line AB345 from some convenient scale of equal parts . 2. Make the angle A37 ° 20 ' . 3 ...
... triangle . EXAMPLE I , In the plane triangle ABC , Given { AB 345 yards BC 232 LA 37 ° 20 ′ ; Required the other parts . Geometrically . 1. Draw the line AB345 from some convenient scale of equal parts . 2. Make the angle A37 ° 20 ' . 3 ...
Seite 16
... triangle ABC , AB 162 chains Ans . Given AC 270 ZB 90 ° ; Required the other parts . EXAMPLE 3 . ZC ZA 53 07 48 BC 216 chains . 36 ° 52 ′ 12 ′′ 32 LA In the plane triangle ABC , Given AB 365 poles ZB 24 ° 45 ′ ZC 98 ° 03 ′ Ans . AC 154 ...
... triangle ABC , AB 162 chains Ans . Given AC 270 ZB 90 ° ; Required the other parts . EXAMPLE 3 . ZC ZA 53 07 48 BC 216 chains . 36 ° 52 ′ 12 ′′ 32 LA In the plane triangle ABC , Given AB 365 poles ZB 24 ° 45 ′ ZC 98 ° 03 ′ Ans . AC 154 ...
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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
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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.