A Treatise of Algebra: Wherein the Principles are Demonstrated ... To which is Added, the Geometrical Construction of a Great Number of Linear and Plane Problems ...M. Carey & sons, 1821 - 408 σελίδες |
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Σελίδα 28
... perpendicular = a , and the base = b , to find the perpendicular ; then ( by what shall hereafter be shown in its proper place ) the answer a2_b2 and is possible , or impossible , ac- 2a will come out cording as the quantity as_b2 2a is ...
... perpendicular = a , and the base = b , to find the perpendicular ; then ( by what shall hereafter be shown in its proper place ) the answer a2_b2 and is possible , or impossible , ac- 2a will come out cording as the quantity as_b2 2a is ...
Σελίδα 247
... perpendicular to BD , but also bi- sects it ( Euc . 3. 3. ) ; whence it is evident that Bm , or Dm , will be the sine of BC or CD , and Om its co - sine ; and that mn , being an arithmetical mean between the sines BE and DG , of the two ...
... perpendicular to BD , but also bi- sects it ( Euc . 3. 3. ) ; whence it is evident that Bm , or Dm , will be the sine of BC or CD , and Om its co - sine ; and that mn , being an arithmetical mean between the sines BE and DG , of the two ...
Σελίδα 249
... perpendicular BC , so is the radius ( of the tables ) to the tangent of the angle at the base . Let DA be the radius to which the table of sines and tangents is adapted , and DE the tangent of the angle A ; then , by reason of the ...
... perpendicular BC , so is the radius ( of the tables ) to the tangent of the angle at the base . Let DA be the radius to which the table of sines and tangents is adapted , and DE the tangent of the angle A ; then , by reason of the ...
Σελίδα 251
... perpendicular falling from the vertical angle . For , Let ABC be the proposed triangle , and BD the perpendicular ; from B as a centre , with the interval BC , let the circumference of a circle be described , cutting the base AC in G ...
... perpendicular falling from the vertical angle . For , Let ABC be the proposed triangle , and BD the perpendicular ; from B as a centre , with the interval BC , let the circumference of a circle be described , cutting the base AC in G ...
Σελίδα 253
... perpendicular BD , opposite the required angle , and suppose DG = AD ; then ( by prop.11 . ) AC : BC + BA :: BC - BA : CG , which subtract- ed from AC , and the remainder di- vided by 2 gives AD ; whence A will be found , by case 2 , of ...
... perpendicular BD , opposite the required angle , and suppose DG = AD ; then ( by prop.11 . ) AC : BC + BA :: BC - BA : CG , which subtract- ed from AC , and the remainder di- vided by 2 gives AD ; whence A will be found , by case 2 , of ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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Δημοφιλή αποσπάσματα
Σελίδα 241 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Σελίδα 53 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Σελίδα 64 - ... then, by adding, or subtracting, the two equations thus obtained, as the case may require, there will arise a new equation, with only one unknown quantity in it, which may be resolved as before.
Σελίδα 251 - ... the sum of the segments of the base is to the sum of the sides as the difference of the sides to the difference of the segments of the base.
Σελίδα 87 - A composition of copper and tin containing 100 cubic inches weighed 505 ounces. How many ounces of each metal did it contain, supposing a cubic inch of copper to weigh of ounces, and a cubic inch of tin to weigh 4т ounces ? Ans. 420 of copper, and
Σελίδα 88 - ... half of what he had left, and half a sheep over ; and, soon after this, a third party met him, and used him in the same manner, and then he had only five sheep left. It is required to find what number of sheep he had at first, Ans, 47 sheep.
Σελίδα 254 - The following particular directions, however, may be of some use. 1st, In preparing the figure, by drawing lines, let them be either parallel or perpendicular to other lines in the figure, or so as to form similar triangles. And if an angle be given, it will be proper to let the perpendicular be opposite to that angle, and to fall from one end of a given line, if possible.