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, Volume 2Printed at the University Press, by WilliamHilliard, 1801 - Mathematics |
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Page 61
... propositions are those of Melius and Archimedes . As 452 355 square of the diameter : area . As 14 11 : square of the diameter : area . If the circumference be given , instead of the diameter , the area may be found as follows : The ...
... propositions are those of Melius and Archimedes . As 452 355 square of the diameter : area . As 14 11 : square of the diameter : area . If the circumference be given , instead of the diameter , the area may be found as follows : The ...
Page 356
... PROPOSITION I , THE squares of the ordinates of the axis are to each other as the rectangles of their abscisses . Let RVB be a plane passing through the axis of the cone ; AEBD another section of the cone perpendicular to the plane RVB ...
... PROPOSITION I , THE squares of the ordinates of the axis are to each other as the rectangles of their abscisses . Let RVB be a plane passing through the axis of the cone ; AEBD another section of the cone perpendicular to the plane RVB ...
Page 358
... , AF FB becomes AF AH HB :: FG * : HI ' , AH :: FG : HI2 , or , in the parabola , the abscisses are to each other , as the squares of their ordinates . PROPOSITION As the PROPOSITION II . square of the transverse axis 358 CONIC SECTIONS .
... , AF FB becomes AF AH HB :: FG * : HI ' , AH :: FG : HI2 , or , in the parabola , the abscisses are to each other , as the squares of their ordinates . PROPOSITION As the PROPOSITION II . square of the transverse axis 358 CONIC SECTIONS .
Page 359
... PROPOSITION II . square of the transverse axis Is to the square of the conjugate So is the rectangle of the abscisses To the square of their ordinate . :: That is , AB ab2 , or Ac ; ac ;; AD DB : DE D E b Q For , by Prop . I. AC CB AD ...
... PROPOSITION II . square of the transverse axis Is to the square of the conjugate So is the rectangle of the abscisses To the square of their ordinate . :: That is , AB ab2 , or Ac ; ac ;; AD DB : DE D E b Q For , by Prop . I. AC CB AD ...
Page 360
... PROPOSITION III . As the square of the conjugate axis : Is to the square of the transverse axis :: So is the rectangle of the abscisses of the conjugate , or the difference of the squares of the semiconjugate and distance of the centre ...
... PROPOSITION III . As the square of the conjugate axis : Is to the square of the transverse axis :: So is the rectangle of the abscisses of the conjugate , or the difference of the squares of the semiconjugate and distance of the centre ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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...
Page 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.
Page 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...
Page 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.
Page 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.
Page 83 - The sphere may be conceived to be formed by the revolution of a semicircle about its diameter, which remains fixed.
Page 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...
Page 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.
Page 38 - Multiply the sum of the two parallel sides by the perpendicular distance between them, and half the product will be the area.