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, المجلد 2Printed at the University Press, by WilliamHilliard, 1801 |
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الصفحة 13
... triangle , the sides are proportional to the sines of their opposite angles . * That is , As one side Is to another ... ABC be any trian- gle in AB assume any point D , take CE = AD , and upon AC demit the perpendiculars DF , EG , BH ; then ...
... triangle , the sides are proportional to the sines of their opposite angles . * That is , As one side Is to another ... ABC be any trian- gle in AB assume any point D , take CE = AD , and upon AC demit the perpendiculars DF , EG , BH ; then ...
الصفحة 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 ...
الصفحة 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 ...
الصفحة 17
... triangle ABC , AC 120 ft . < B 64 ° 34 ′ 21 ′′ . Given BC 112 ft . 115 25 39 LA 57 ° 27 ' ; Ans . ZC 57 58 39 Req . the other parts . 7 07 21 AB S11265 feet . 16:47 PROBLEM II . Given two sides and the angle included by them ; to find ...
... triangle ABC , AC 120 ft . < B 64 ° 34 ′ 21 ′′ . Given BC 112 ft . 115 25 39 LA 57 ° 27 ' ; Ans . ZC 57 58 39 Req . the other parts . 7 07 21 AB S11265 feet . 16:47 PROBLEM II . Given two sides and the angle included by them ; to find ...
الصفحة 19
... triangle ABC , Given { AB 345 yards , AC 174 07 yd . ZA 37 ° 20 ′ ; Required the other parts . A Geometrically . 1. Draw AB equal to 345 , from a scale of equal parts . 2. Make the angle A equal to 37 ° . 20 . 3. Make AC equal to 174'07 ...
... triangle ABC , Given { AB 345 yards , AC 174 07 yd . ZA 37 ° 20 ′ ; Required the other parts . A Geometrically . 1. Draw AB equal to 345 , from a scale of equal parts . 2. Make the angle A equal to 37 ° . 20 . 3. Make AC equal to 174'07 ...
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عبارات ومصطلحات مألوفة
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
مقاطع مشهورة
الصفحة 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.
الصفحة 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...
الصفحة 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.
الصفحة 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...
الصفحة 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.
الصفحة 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.
الصفحة 83 - The sphere may be conceived to be formed by the revolution of a semicircle about its diameter, which remains fixed.
الصفحة 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...
الصفحة 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.
الصفحة 38 - Multiply the sum of the two parallel sides by the perpendicular distance between them, and half the product will be the area.