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 18
... continued to an Infinite Series : But if , after you have plac'd as many Terms in the Quotient as you think proper , you have a Mind to have the exact Quo- tient , place the laft Remainder over your Divifor , with a Line between them ...
... continued to an Infinite Series : But if , after you have plac'd as many Terms in the Quotient as you think proper , you have a Mind to have the exact Quo- tient , place the laft Remainder over your Divifor , with a Line between them ...
Page 47
... continued to an endless Series ; thus , 2. Let it be required to Extract the Square - Root of rr + z nearly . = 4 4-3n . And ( i . c . 2d . y ) = x .. O Remainder . Operation . Tr KK 24 + 27 873 16rs 528 128r ? ' & c . Sine Fine . rr ...
... continued to an endless Series ; thus , 2. Let it be required to Extract the Square - Root of rr + z nearly . = 4 4-3n . And ( i . c . 2d . y ) = x .. O Remainder . Operation . Tr KK 24 + 27 873 16rs 528 128r ? ' & c . Sine Fine . rr ...
Page 64
... continued to as many , or almost as many Figures , as the next preceding x bath of the firft Fi- gures of the Root fought ; as in the following Examples . Example 1 . If a3 = 231 ; Quere a proxime . Suppofe x + y = a ; then ( a3 = ) x3 ...
... continued to as many , or almost as many Figures , as the next preceding x bath of the firft Fi- gures of the Root fought ; as in the following Examples . Example 1 . If a3 = 231 ; Quere a proxime . Suppofe x + y = a ; then ( a3 = ) x3 ...
Page 68
... 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 Part . V : Of the Indices of Powers.
... 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 Part . V : Of the Indices of Powers.
Page 69
... continued backward , that the feveral Terms of it will be found ( by Subtracting from the Index of the Root a ' the common Excefs of the Indices , to wit 1 , and from the Remainder o the faid common Excefs , and from this Remainder 1 ...
... continued backward , that the feveral Terms of it will be found ( by Subtracting from the Index of the Root a ' the common Excefs of the Indices , to wit 1 , and from the Remainder o the faid common Excefs , and from this Remainder 1 ...
Other editions - View all
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...