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 69
... divided by perpendicular chords into 1000 equal parts , and is at the end of MENSURATION . The reason of the rule itself depends upon this property →→→ That the versed sines of similar segments are as the diameters of the circles ...
... divided by perpendicular chords into 1000 equal parts , and is at the end of MENSURATION . The reason of the rule itself depends upon this property →→→ That the versed sines of similar segments are as the diameters of the circles ...
Seite 84
... divided by the transverse . 2. To aD2 ad2 D3 3 And therefore x -x . = 3a x D ' D'd2 area of the frustum . Q. E. D. * DEMONSTRATION . Let semitransverse axe , c≈ semi- conjugate , xordinate , and y = abscissa . Then will yx : 1+ a2 a2 + ...
... divided by the transverse . 2. To aD2 ad2 D3 3 And therefore x -x . = 3a x D ' D'd2 area of the frustum . Q. E. D. * DEMONSTRATION . Let semitransverse axe , c≈ semi- conjugate , xordinate , and y = abscissa . Then will yx : 1+ a2 a2 + ...
Seite 85
... divided by the transverse . 3. To each of the products , thus found , add 15 times the parameter , and divide the former by the latter ; then , this quotient , being multiplied by the ordinate , will give the length of the arc nearly ...
... divided by the transverse . 3. To each of the products , thus found , add 15 times the parameter , and divide the former by the latter ; then , this quotient , being multiplied by the ordinate , will give the length of the arc nearly ...
Seite 97
... divided into a number of little squares , each equal to the super- ficial measuring unit . Then will those squares be the bases of a like number of small cubes , which are each equal to the solid measuring unit . But the number of ...
... divided into a number of little squares , each equal to the super- ficial measuring unit . Then will those squares be the bases of a like number of small cubes , which are each equal to the solid measuring unit . But the number of ...
Seite 106
... divided by their difference , or by the sum arising from the square of their half differ- ence added to 3 times the square of their half sum . 3. And in the frustum of a cone , the mean area is found by multiplying 2618 , or of 7854 ...
... divided by their difference , or by the sum arising from the square of their half differ- ence added to 3 times the square of their half sum . 3. And in the frustum of a cone , the mean area is found by multiplying 2618 , or of 7854 ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
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.