A Treatise of Algebra in Two Books: The First Treating of the Arithmetical, and the Second of the Geometrical Part |
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Page 68
... Ratio is the 1ft . Power or Root a , and the Indices of thofe Powers in a continued Arithmetical Proportion , whofe com- non Excefs is 1 , by the Definitions of both Proportions . Now , 1 Now , fince the Exponent of each Power of the 68 ...
... Ratio is the 1ft . Power or Root a , and the Indices of thofe Powers in a continued Arithmetical Proportion , whofe com- non Excefs is 1 , by the Definitions of both Proportions . Now , 1 Now , fince the Exponent of each Power of the 68 ...
Page 69
... Ratio , and this Quotient by the faid Ratio , and this Quotient a a3 I a by the said Ratio , & c . ) = & c . 11 , 1 , 1 , 1 , a , a2 , a3 , aa , & c . From the two last Paragraphs , it is manifeft that ao is = 1 , alfo = —— , alfo a — 2 ...
... Ratio , and this Quotient by the faid Ratio , and this Quotient a a3 I a by the said Ratio , & c . ) = & c . 11 , 1 , 1 , 1 , a , a2 , a3 , aa , & c . From the two last Paragraphs , it is manifeft that ao is = 1 , alfo = —— , alfo a — 2 ...
Page 72
... Ratio or Pro- portion to one another , may be exprefs'd by Rational Numbers or Quantities : And fuch Surd - Roors whofe Ratio cannot be exprefs'd by Rati onal Numbers or Quantities are call'd Incommenfurable . CHAP . O CHA P. II ...
... Ratio or Pro- portion to one another , may be exprefs'd by Rational Numbers or Quantities : And fuch Surd - Roors whofe Ratio cannot be exprefs'd by Rati onal Numbers or Quantities are call'd Incommenfurable . CHAP . O CHA P. II ...
Page 77
... Ratio of b2 to c2 ; that is bb :: cc . b C :: This may be demonftrated by Equating the Product of the Extreams to that of the Means ; thus , b C 7 x = 7 x x c4 is equal the Product of the Ex- treams . And And xbb = ਵੀ = ਲ 641 _b_c3b ...
... Ratio of b2 to c2 ; that is bb :: cc . b C :: This may be demonftrated by Equating the Product of the Extreams to that of the Means ; thus , b C 7 x = 7 x x c4 is equal the Product of the Ex- treams . And And xbb = ਵੀ = ਲ 641 _b_c3b ...
Page 99
... Ratio , and fhews the Habitude or Relation the Numbers or Quantities have to one another ; viz . whether they are ... Ratio ; but Note that r must be I Lemma . If from the Sum of any Series in Terms be fucceffively Subtracted ; I fay the ...
... Ratio , and fhews the Habitude or Relation the Numbers or Quantities have to one another ; viz . whether they are ... Ratio ; but Note that r must be I Lemma . If from the Sum of any Series in Terms be fucceffively Subtracted ; I fay the ...
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A Treatise of Algebra: In Two Books; The First Treating of the Arithmetical ... Philip Ronayne No preview available - 2017 |
A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ... PHILIP. RONAYNE No preview available - 2018 |
Common terms and phrases
Adfected Affirmative alfo alſo Angle Anſwer Area becauſe Binomial Cafe Canon Chap circumfcribing Co-efficient Co-fine common confequently Cube-Root Demonftration Denominator Diſtances Divided Divifion Divifor Elem equal Eucl faid fame fecond Term fhall figurate Number fimilar fince firft Term firſt fmall fome foregoing fought Fraction ftraight Line fuch fuppos'd greater greateſt hath indefinitely little Index infcribed Integer Intereft interfecting laft laſt leaft leffer lefs Lemma Logarithm Meaſure Multiplyed muſt Number of Alternations Power PROB produc'd PROP Quadratick Quantity Queſtion Quotient Radius Ratio Rational Theorem reduc'd Refidual Refolvend refpectively Remainder required to find Root Scholia Scholium Series Side Sine Square Square-Root Step Subtract Suppofe Surds Tangent thefe Theorem theſe thofe Trapezium Uncia univerfal Value Whence wherefore whofe whole Numbers
Popular passages
Page 334 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 326 - 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, fourths, &c.
Page 32 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 332 - Radius, fo the other Sides acquire different Names, which Names are either Sines, Tangents, or Secants, and are to be taken out of your Table, To find a Side, any Side may be made Radius : Then fay, as the Name of the Side given is to the Name of the Side required ; fo is the Side given to the Side required.
Page 8 - ... 1. If equal quantities be added to equal quantities, the sums will be equal. 2. If equal quantities be subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by equal quantities, the products will be equal. 4. If equal quantities be divided by equal quantities, the quotients will be equal. 5.
Page 34 - Multiply the numerator of the dividend by the denominator of the divisor, for a numerator; and multiply the denominator of the dividend by the numerator of the divisor, for a denominator 19.
Page 333 - In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C...
Page 327 - Every plane triangle consists of six parts ; viz., three sides and three angles ; any three of which being given (except the three angles), the other three may be readily found by logarithmical calculation.
Page 327 - Parts, viz. three Sides and three, Angles : Any three of which being given, except the three Angles of a Plane Triangle, the other three may be found either Mechanically, by the help of a Scale of equal Parts and Line of Chords, or by an...