A Treatise of Algebra in Two Books: The First Treating of the Arithmetical, and the Second of the Geometrical Part |
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... + 4 + 3 Divided by 9 . The like Demonstration may evidently be applyed as well to any other Number as to 3467 . Q. E. D. See the following Notation . Scholium Scholium . From the foregoing Demonftration it is evident that i INTRODUCTION .
... + 4 + 3 Divided by 9 . The like Demonstration may evidently be applyed as well to any other Number as to 3467 . Q. E. D. See the following Notation . Scholium Scholium . From the foregoing Demonftration it is evident that i INTRODUCTION .
Page 197
... say that 223- | - nn - | - n is to their Sum 21 + 4 + 9 + - 16- | - & c . - | - nn . 2 2 3 DE- DEMONSTRATION , zis- It is manifeft that z is to How to raise Canons for finding Sums of the Powers of an Arithmetical Pro- greffion continu'd.
... say that 223- | - nn - | - n is to their Sum 21 + 4 + 9 + - 16- | - & c . - | - nn . 2 2 3 DE- DEMONSTRATION , zis- It is manifeft that z is to How to raise Canons for finding Sums of the Powers of an Arithmetical Pro- greffion continu'd.
Page 198
... DEMONSTRATION , zis- It is manifeft that z is to the Difference of the Sums of the two next following Series ; each of whose Ranks is the Sum of an , viz . Greater Series . 1-—2—3- | -4- | - & c.- | -n 1-1-2-1-3-1-4 + & c . - + n 1 ...
... DEMONSTRATION , zis- It is manifeft that z is to the Difference of the Sums of the two next following Series ; each of whose Ranks is the Sum of an , viz . Greater Series . 1-—2—3- | -4- | - & c.- | -n 1-1-2-1-3-1-4 + & c . - + n 1 ...
Page 199
... ( as 13 , 23 , 33 , 43 , & c . n3 ) n I say that 24 +223 + nn is equal to their Sums , that is = 4 7+ 8 + 27 +64 + & c . + 223 . DE- DEMONSTRATION . The Sum ≈ is manifeftly equal to the of an Arithmetical Progreffion continued . 199.
... ( as 13 , 23 , 33 , 43 , & c . n3 ) n I say that 24 +223 + nn is equal to their Sums , that is = 4 7+ 8 + 27 +64 + & c . + 223 . DE- DEMONSTRATION . The Sum ≈ is manifeftly equal to the of an Arithmetical Progreffion continued . 199.
Page 200
... DEMONSTRATION . The Sum ≈ is manifeftly equal to the Difference of the Sums of the greater and leffer following Series , each of whose Ranks is the Sum of the Squares of an- , viz . Greater Series . 1 + 4 + 9 + 16 + & c .-- 222 + 4 + 9 ...
... DEMONSTRATION . The Sum ≈ is manifeftly equal to the Difference of the Sums of the greater and leffer following Series , each of whose Ranks is the Sum of the Squares of an- , viz . Greater Series . 1 + 4 + 9 + 16 + & c .-- 222 + 4 + 9 ...
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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...