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 4
... Extracting of Roots . Irrationality , or the Sign of a Surd - Root . Therefore . ( b More c , or c added to b . b ... Extracted out of it . 2 √b , ( or √ b ) , ↓ b , ↓ b , c . Signifie the Square - Root of b , the Cube - Root of b ...
... Extracting of Roots . Irrationality , or the Sign of a Surd - Root . Therefore . ( b More c , or c added to b . b ... Extracted out of it . 2 √b , ( or √ b ) , ↓ b , ↓ b , c . Signifie the Square - Root of b , the Cube - Root of b ...
Page 44
... Extracted . If the given Powers have Co - efficients ( viz . Numbers prefix'd to them ) then you must Extract their respective Roots . Thus 1 1814412964868 [ 20736a + b + c + I 22 9a2 36a4b + 144a2bc2 Ius 43 за 6ab2 12abc 200214 за ...
... Extracted . If the given Powers have Co - efficients ( viz . Numbers prefix'd to them ) then you must Extract their respective Roots . Thus 1 1814412964868 [ 20736a + b + c + I 22 9a2 36a4b + 144a2bc2 Ius 43 за 6ab2 12abc 200214 за ...
Page 45
... Extracted out of both Co - efficients and Indices of the given Power , then it is a Surd , and must have the Sign of ... Extracted requires ; that is , to the fecond Power , if it be the Square - Root ; to the third Power , if it be the ...
... Extracted out of both Co - efficients and Indices of the given Power , then it is a Surd , and must have the Sign of ... Extracted requires ; that is , to the fecond Power , if it be the Square - Root ; to the third Power , if it be the ...
Page 46
... Extracted in an easier , but more tedious Manner ; thus , a2 - 6an9nn 242 xx - 6nz + zz ( 43n + z Root . 6an + 9nn + 2az — 6nz - \ - zz Refolvend . Divifor 2a = 2x - Ablass Ablat . 6an = 2xy + gnn = yy + 46 Evolution .
... Extracted in an easier , but more tedious Manner ; thus , a2 - 6an9nn 242 xx - 6nz + zz ( 43n + z Root . 6an + 9nn + 2az — 6nz - \ - zz Refolvend . Divifor 2a = 2x - Ablass Ablat . 6an = 2xy + gnn = yy + 46 Evolution .
Page 51
... Extracted ; and the Power thus produc'd is your Canon for Evolving . But when you are to Extract any of the Roots of an Adfected Equation , fuppofe the Binomial x + y = the Root you feek ; then instead of the faid Root ( or unknown ...
... Extracted ; and the Power thus produc'd is your Canon for Evolving . But when you are to Extract any of the Roots of an Adfected Equation , fuppofe the Binomial x + y = the Root you feek ; then instead of the faid Root ( or unknown ...
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...