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, Τόμος 2Printed at the University Press, by WilliamHilliard, 1801 |
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Σελίδα 39
... the parallel sides . being 21 feet 3 inches and 18 feet 6 inches , and the dis- tance between them 8 feet 5 inches . Ans . 167 feet 3 inches 4 " 6 " " . PROBLEM PROBLEM V. To find the area of a trapezium . ENSURATION OF SUPERFICIES F.
... the parallel sides . being 21 feet 3 inches and 18 feet 6 inches , and the dis- tance between them 8 feet 5 inches . Ans . 167 feet 3 inches 4 " 6 " " . PROBLEM PROBLEM V. To find the area of a trapezium . ENSURATION OF SUPERFICIES F.
Σελίδα 40
... trapezium . CASE I. For any trapezium RULE . Divide it into two triangles by a diagonal ; then find the areas of these triangles , and add them together . Or , if two perpendiculars be let fall on the diagonal from the other two ...
... trapezium . CASE I. For any trapezium RULE . Divide it into two triangles by a diagonal ; then find the areas of these triangles , and add them together . Or , if two perpendiculars be let fall on the diagonal from the other two ...
Σελίδα 41
... trapezium of the above description , if any two adjacent sides be multiplied together , and also the other two ; and if the sum of these two products be multiplied by the sine of the angle , included by either of the pairs of sides ...
... trapezium of the above description , if any two adjacent sides be multiplied together , and also the other two ; and if the sum of these two products be multiplied by the sine of the angle , included by either of the pairs of sides ...
Σελίδα 42
... trapezium ABDE , the diag onal BE being 42 , the perpendicular DF 18 , and the per- pendicular AC 16 . 18 16 34 42 C B F F 68 136 2 ) 1428 714 the answer . 2. In But , by right - angled triangles , BS ' + SD ' DT + TB ' , that is , dd + ...
... trapezium ABDE , the diag onal BE being 42 , the perpendicular DF 18 , and the per- pendicular AC 16 . 18 16 34 42 C B F F 68 136 2 ) 1428 714 the answer . 2. In But , by right - angled triangles , BS ' + SD ' DT + TB ' , that is , dd + ...
Σελίδα 43
... trapezium ABDE , the side BD is 15 , DE 13 , EA 14 , AB 12 , and the diagonal BE is 16 : required the area . AC 16 AB 15 BC 13 AC 16 CD 14 AD 12 2944 sum 22 22 22 2 ) 42 21 21 21 16 15 ២ 13 16 14 12 679 ། ཨཱུ ། 42 5 7 0 7 35 9 378 22 ...
... trapezium ABDE , the side BD is 15 , DE 13 , EA 14 , AB 12 , and the diagonal BE is 16 : required the area . AC 16 AB 15 BC 13 AC 16 CD 14 AD 12 2944 sum 22 22 22 2 ) 42 21 21 21 16 15 ២ 13 16 14 12 679 ། ཨཱུ ། 42 5 7 0 7 35 9 378 22 ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 83 - The sphere may be conceived to be formed by the revolution of a semicircle about its diameter, which remains fixed.
Σελίδα 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...
Σελίδα 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.
Σελίδα 38 - Multiply the sum of the two parallel sides by the perpendicular distance between them, and half the product will be the area.