A Treatise of Algebra, in Three Parts: Containing I. The Fundamental Rules and Operations; II. The Composition and Resolution of Equations of All Degrees, and the Different Affections of Their Roots; III. The Application of Algebra and Geometry to Each Other. To which is Added an Appendix Concerning the General Properties of Geometrical LinesA. Millar and J. Nourse, 1756 - 432 páginas |
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Página 5
... remainder becomes of the oppofite kind . Thus if we add the lines AB and BD to- gether , their fum is AD ; A C B D but if we are - + . A B to fubtract B C D from AB , then BC BD is to be taken the contrary way towards A , and the remainder ...
... remainder becomes of the oppofite kind . Thus if we add the lines AB and BD to- gether , their fum is AD ; A C B D but if we are - + . A B to fubtract B C D from AB , then BC BD is to be taken the contrary way towards A , and the remainder ...
Página 9
... remainder , and fubjoin the common letter or let- ters . EXAMPLES . To 4a 6c Add + 7a 36 + 8c Sum + 3a 26+ 20 Το a + 6x - 5y + 8 2a 26 2a + 2b Add5a - 4x + 4y - 3 Sum - — 4a + 2x y + 5 This rule is easily deduced from the nature of ...
... remainder , and fubjoin the common letter or let- ters . EXAMPLES . To 4a 6c Add + 7a 36 + 8c Sum + 3a 26+ 20 Το a + 6x - 5y + 8 2a 26 2a + 2b Add5a - 4x + 4y - 3 Sum - — 4a + 2x y + 5 This rule is easily deduced from the nature of ...
Página 11
... remainder . For , to subtract any quantity , either pofitive or negative , is the fame as to add the oppofite kind . EXAMPLES . From + 5a 8a 73 Şubtract + 3a 3a + 4b Remaind . 5a - 3a , or 2a --- 5a . 11b From 24 --- 3x + 56 Subtract 6a ...
... remainder . For , to subtract any quantity , either pofitive or negative , is the fame as to add the oppofite kind . EXAMPLES . From + 5a 8a 73 Şubtract + 3a 3a + 4b Remaind . 5a - 3a , or 2a --- 5a . 11b From 24 --- 3x + 56 Subtract 6a ...
Página 19
... remainder , the divifion is finished : If there is a remainder , you are to proceed after the fame manner till no remainder is left ; or till it appear that there will be always fome remainder . Some Examples will illuftrate this ...
... remainder , the divifion is finished : If there is a remainder , you are to proceed after the fame manner till no remainder is left ; or till it appear that there will be always fome remainder . Some Examples will illuftrate this ...
Página 25
... remainder fet over the deno- minator shall be the fractional part . Thus = 23 ; 12 ab + a2 a2 ax + 2xx 5 b = a + ; b a + x x2 aa + xx 2xx + * = a + x + ax AX C 4 PRO- PROBLEM III . § 26. To reduce fractions of different Chap . 6 . 25 ...
... remainder fet over the deno- minator shall be the fractional part . Thus = 23 ; 12 ab + a2 a2 ax + 2xx 5 b = a + ; b a + x x2 aa + xx 2xx + * = a + x + ax AX C 4 PRO- PROBLEM III . § 26. To reduce fractions of different Chap . 6 . 25 ...
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Pasajes populares
Página 74 - AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C.
Página 55 - A privateer running at the rate of 10 miles an hour discovers a ship 18 miles off making way at the rate of 8 miles an hour : how many miles can the ship run before being overtaken ? Ans.
Página 107 - ... -{-24, equal to nothing, according to the propofed equation. And it is certain that there can be no other values of x...
Página 367 - This is a quarto volume, containing xxxii + 38 pages, and three plates of figures. The title points out that the work consists of two parts ; we are principally concerned with the first part : on...
Página 193 - The demonftration is deduced from the laft article, as the 7 8th is from the preceding. CHAP. IX. Of the Methods by which you may approximate to the roots of numeral Equations by their limits. §84. TT 7 HEN any equation is propofed W to be refolved, firft find the limits of the roots (by Chap. 5.) as for example...
Página 22 - Rule. Multiply the numerator of the dividend by the denominator of the divifor, their produit ¡hall give the numerator of the quotient. 'Then multiply t be denominator of the' dividend by the numerator of the divifor, and their predu£f jhall give the denominator.