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 13
... - B E D al radius AD or CE . Now from similar triangles we shall SAB : BH :: AD : DF CB : BH :: have AD ( CE ) & : EG } and hence , of equality , AB BC :: EG : DF . The degrees , in the acute angle ; and if PLANE TRIGONOMETRY . 33.
... - B E D al radius AD or CE . Now from similar triangles we shall SAB : BH :: AD : DF CB : BH :: have AD ( CE ) & : EG } and hence , of equality , AB BC :: EG : DF . The degrees , in the acute angle ; and if PLANE TRIGONOMETRY . 33.
Página 22
... Hence , in each of the right - angled triangles , will be known two sides , and the angle opposite to one of them ; and consequently the other angles will be found by the first problem . NOTE . In the above proportions , if half the ...
... Hence , in each of the right - angled triangles , will be known two sides , and the angle opposite to one of them ; and consequently the other angles will be found by the first problem . NOTE . In the above proportions , if half the ...
Página 23
... Hence , = 206 ° 59 = BP . 13841 AP . 2 And 345-68-18 Then , in the triangle APC , right - angled at P , As AC To AP So S. P To S. ZACP 174'07 138.41 90 ° 00 ' 52 40 Which , being taken from 90 00 Leaves 37 20 LA . 2 * 2407239 2 ...
... Hence , = 206 ° 59 = BP . 13841 AP . 2 And 345-68-18 Then , in the triangle APC , right - angled at P , As AC To AP So S. P To S. ZACP 174'07 138.41 90 ° 00 ' 52 40 Which , being taken from 90 00 Leaves 37 20 LA . 2 * 2407239 2 ...
Página 41
... BA . as BS , T D Then 1 : { a 8 b : And I 5S :: bs = BT , a : a√1-55AS , [ b b√ 1 — 55 = CT ; Hence SD = d + ay 1 — ss , and DT - 61 — ss . VOL . II . But , EXAMPLES . 1. To find the area of the trapezium MENSURATION OF SUPERFICIES . 41.
... BA . as BS , T D Then 1 : { a 8 b : And I 5S :: bs = BT , a : a√1-55AS , [ b b√ 1 — 55 = CT ; Hence SD = d + ay 1 — ss , and DT - 61 — ss . VOL . II . But , EXAMPLES . 1. To find the area of the trapezium MENSURATION OF SUPERFICIES . 41.
Página 43
... Hence be deduced Rule 2 , for the triangle ; may for , if we here suppose one of the sides , as d , to be nothing , or to decrease till it vanish , the rule will become s — axs — b Xs — c Xs , the same as in the triangle . COR 3. If a ...
... Hence be deduced Rule 2 , for the triangle ; may for , if we here suppose one of the sides , as d , to be nothing , or to decrease till it vanish , the rule will become s — axs — b Xs — c Xs , the same as in the triangle . COR 3. If a ...
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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.