A Treatise of Algebra: Wherein the Principles are Demonstrated and Applied ... To which is Added, the Geometrical Construction of a Great Number of Linear and Plane Problems; with the Method of Resolving the Same Numerically |
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Page 249
... base . a- E F Let DA be the radius to which the table of fines and tangents is dapted , and DE the tangent of the an- gle A ; then , by rea- fon of the fimilarity of the triangles ABC and ADE , it will be , as AB BC :: AD : DE . 2 ...
... base . a- E F Let DA be the radius to which the table of fines and tangents is dapted , and DE the tangent of the an- gle A ; then , by rea- fon of the fimilarity of the triangles ABC and ADE , it will be , as AB BC :: AD : DE . 2 ...
Page 260
... base AD and BD , and the ratio of the fides AC and BC of any plane triangle ABC , being given ; to find the fides . C Put AD a , BD = by AC x ; and let the given ratio of AC to BC , be as m to n , fo fhall BC = nx - m But ACAD2 ( = DC3 ) ...
... base AD and BD , and the ratio of the fides AC and BC of any plane triangle ABC , being given ; to find the fides . C Put AD a , BD = by AC x ; and let the given ratio of AC to BC , be as m to n , fo fhall BC = nx - m But ACAD2 ( = DC3 ) ...
Page 266
... base ; to find the fides aud angles of the triangle . G C Conceive a circle to be defcribed about the triangle , and let EG be a diameter of that circle , cutting the bafe AB perpendicularly in F ; alfo from the cen- ter O , fuppofe OA ...
... base ; to find the fides aud angles of the triangle . G C Conceive a circle to be defcribed about the triangle , and let EG be a diameter of that circle , cutting the bafe AB perpendicularly in F ; alfo from the cen- ter O , fuppofe OA ...
Page 267
... base AB ; whence AO and F will be both given , by plane trigonometry , and confequently EF ( ÃO — FO ) and EG ( = 2AO ) . Call , therefore , EF = a , EG = b , CD = c , and DE = x ; and fup- pofe CG to be drawn ; then , the angle ECG ...
... base AB ; whence AO and F will be both given , by plane trigonometry , and confequently EF ( ÃO — FO ) and EG ( = 2AO ) . Call , therefore , EF = a , EG = b , CD = c , and DE = x ; and fup- pofe CG to be drawn ; then , the angle ECG ...
Page 269
... base BD = a , · the bifecting line CD b , and the perpendicular CQ ( DE ) : then , fince ( by Euc . 20. A E B D Q 3. ) the angle BFD is equal to ACB , it will ( by plane tri- gonometry ) be , as m ( fine of BFD ) : a ( DB ) :: n ( fine ...
... base BD = a , · the bifecting line CD b , and the perpendicular CQ ( DE ) : then , fince ( by Euc . 20. A E B D Q 3. ) the angle BFD is equal to ACB , it will ( by plane tri- gonometry ) be , as m ( fine of BFD ) : a ( DB ) :: n ( fine ...
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A Treatise of Algebra: Wherein the Principles Are Demonstrated ... to Which ... Thomas Simpson No preview available - 2013 |
Common terms and phrases
alfo alſo annuity anſwers arch arifing ax² bafe baſe becauſe bifect cafe circle co-fine coefficient confequently CONSTRUCTION defcribe denoted difference divided divifor draw E. D. Method equal equation expreffed expreffion faid fame manner fecond fegments feries feven fides fign fimilar fimple fince firft firſt fo fhall folution fome fquare root ftand fubftituted fubtracted fuch fuppofing given angle given ratio intereft interfecting laft laſt leaft leffer lefs likewife Method of Calculation moidores muft multiplied muſt number of terms obferved parallel perpendicular pofitive PROBLEM progreffion propofed quantities queftion quotient radius raiſe reafon rectangle refpectively reprefented right-line ſhall tangent thefe thence Theorem theſe thofe thoſe trapezium triangle triangle ABC uſe whence whereof whofe whole number
Popular passages
Page 47 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 229 - 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, etc.
Page 57 - Quantities is the least involved, and let the Value of that Quantity be found in each Equation by the Rules already given), looking upon all the Rest as known : let the Values thus found be put equal to each other (for they are equal...
Page 19 - We have seen that multiplying by a whole number is taking the multiplicand as many times as there are units in the multiplier.
Page 28 - EXAMPLES. • 1. If the fractions to be divided have a common denominator, take the numerator of the dividend for a new numerator, and the numerator of the divisor for the new denominator.
Page 44 - ... the said numerator or denominator (whichever it is) into two parts, so that the said letter may be found in every term of the one part, and be totally excluded out of the other ; this being done, let the greatest common divisor of these two parts be found, which will evidently be a divisor to the whole, and by which the division of the...
Page 217 - SIMPLE Intereft, is that which is paid for the Loan of any Principal or Sum of Money, lent out for fome Time, at any...
Page 223 - R% the amount of one pound in two years ; and therefore as I to R, fo is R% the fum forborn the third year, to R3, the amount in three years : whence it appears that R", or R raifed to the power whofe exponent is the number of years, will be the amount of one pound in thofe years. But >as i A is to its amount R", fo is P to ( a) its amount, in the fame time ; whence we have PX R" =r a. Moreover, becaufe the amount of one pound, in nyears, is R", its increafe in that time will be R...
Page 230 - BI, the sine of its complement HB. The tangent of an arc, is a right line touching the circle in one extremity of that arc, continued from thence to meet a line drawn from the...
Page 66 - ... the product of the extremes divided by either mean will give the other mean, and the product of the means divided by either extreme will give the other extreme.