Some General Theorems of Considerable Use in the Higher Parts of MathematicsW. Sands, A. Murray, and J. Cochran, 1746 - 163 من الصفحات |
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2n powers bafe baſe becauſe centre circle let circumference cone cubes defcribed diameter diculars drawn diſtance drawn in given drawn perpendiculars drawn right lines eighth powers ellipfe equal to twice Eucl fame number fame ratio fecond fegment femidiameter figure circumfcribed firlot firſt fition fixth powers folid content fourth power fphere fruftum fuch fuppofed furface given angles given by pofition given magnitudes Gunter's chain gure height let the fum Let the number likewiſe line drawn lines in given meaſured number greater number less number of fides number of right obfervator parallel pentagon perpendi perpendicu perpendiculars drawn pints pofi point let point of interfection poſition prop PROPOSITION ratio that OA rectangle contained regular figure right lines found right lines given SCHOLIUM ſquare ſtation ſum theorem theſe thoſe three lines found three right lines tion triangle twice the fum twice the multiple uſe veffel whofe
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الصفحة 65 - Figure circumscrib'd about a Circle " and from any point in the Circumference of the Circle let there be " drawn perpendiculars to the...
الصفحة 75 - ... be equal to the multiple by the number of the fides of the figure of the fourth power of the femidiameter of the circle, together with four times the multiple by the fame number of the fourth power...
الصفحة 74 - LET there be any regular figure inscribed in a circle ? and from all the angles of the figure, let there be drawn right lines to any point in the circumference of the circle : the sum of the fourth powers of the chords will be equal to six times the multiple of the fourth power of the radius of the circle, by the number of the sides of the figure.
الصفحة 77 - ... of the products, taken two at a time, of the squares of the lines drawn from the angles of a triangle to the middle points of the opposite sides, is equal to nine times the sum of the products, taken two at a time, of the squares of the sides. Equation [10] gives this THEOREM. Sixteen times the sum of the fourth powers of the lines drawn from the angles of a triangle to the middle points of the opposite sides, is equal to nine times the sum of the fourth powers of the sides.
الصفحة 8 - If the circumference of a circle be divided into any number of equal parts, the chords joining the successive points of division form a regular polygon inscribed in the circle ; and the tangents drawn at the points of division form a regular polygon circumscribed about the circle.
الصفحة 51 - ... a point may be found, fuch, that if from any point there be drawn perpendiculars to all the fides of the figures, and a ftraight line to the point found, twice the fum of the fquares of the perpendiculars will be equal to the multiple of the line drawn to the point found, by the number of the fides, together with a given fpace.
الصفحة 133 - Cor. Let there be any number of right lines given by pofition ; three right lines may be found that will be given by pofition, fuch, that if from any point there be drawn right lines in given angles to all the right lines given by pofition, and likewife there be drawn...
الصفحة 52 - ... fector), by which an arch may be made of a given number of degrees to any radius. The quantities of angles are likewife determined by other lines ufually marked upon rules, as the lines of fines, tangents, and fecants ; but as thefe methods are not fo eafy or fo proper in this place, we omit them. To delineate figures fimilar or like to others given, befides the equality of the angles, the fame proportion is to be preferved among the fides of the figure that is to to be delineated, as is among...
الصفحة 120 - It is no less easy to 6nd the solid content of a given pyramid ; for the area of the base being found, let it be multiplied by the third part of the height of the pyramid, or the third part of the base by the height, and the product will give the solid content, as is demonstrated by Euclid, lib.
الصفحة 12 - Let there be two circles having the fame centre, and let the circumference of one of the circles be divided into any number of equal parts, and from the points of...