A Treatise of Algebra in Two Books: The First Treating of the Arithmetical, and the Second of the Geometrical PartW. Innys, 1717 - 408 σελίδες |
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Σελίδα 37
... also ) of every fingle Power , how high foever it be , is an Unit or ( which neither Multiplies nor Divides ) and all the Powers of any Binomial of Refidual Root are naturally raised by Multiplying of the Precedent Power into its ...
... also ) of every fingle Power , how high foever it be , is an Unit or ( which neither Multiplies nor Divides ) and all the Powers of any Binomial of Refidual Root are naturally raised by Multiplying of the Precedent Power into its ...
Σελίδα 61
... Also the Cube - Root of 1+ a3 + 3a2b + zab2 + b3 a3 — 3a2b + 3ab2 — b3 b 6a2b + 2b3 b a3 34'b + 3ab2 — b2 a + b a 3a3b will be found = Sect . 2. Evolution of Fragional Numbers . If the Fractional Numbers given can be reduc'd to Decimals ...
... Also the Cube - Root of 1+ a3 + 3a2b + zab2 + b3 a3 — 3a2b + 3ab2 — b3 b 6a2b + 2b3 b a3 34'b + 3ab2 — b2 a + b a 3a3b will be found = Sect . 2. Evolution of Fragional Numbers . If the Fractional Numbers given can be reduc'd to Decimals ...
Σελίδα 68
... also 4-1 I allo a I a3 == ‚ · also 4-2 = & c . And that the said Series being con- tinued backward and forward , may be writ Thus & c . 4 - 1 , a - 2 , a - 1 , a ° , a ' , a ' , a3 , - & c . I I Or thus & c , • a3 1 , a ' , q3 , a3 ...
... also 4-1 I allo a I a3 == ‚ · also 4-2 = & c . And that the said Series being con- tinued backward and forward , may be writ Thus & c . 4 - 1 , a - 2 , a - 1 , a ° , a ' , a ' , a3 , - & c . I I Or thus & c , • a3 1 , a ' , q3 , a3 ...
Σελίδα 69
... Also the Exponent of the Quotient of a3 Divided by a3 is prov'd to be 3-5 = 2 ; thus -- as a3 - a2 a3 a - 2 ( by what has been prov'd in this Part V. ) In like manner the Exponent of the Quotient of a - 4 Divided by a - 3 is prov'd to + ...
... Also the Exponent of the Quotient of a3 Divided by a3 is prov'd to be 3-5 = 2 ; thus -- as a3 - a2 a3 a - 2 ( by what has been prov'd in this Part V. ) In like manner the Exponent of the Quotient of a - 4 Divided by a - 3 is prov'd to + ...
Σελίδα 72
... also a Fraction , ( by the 16. 8. Eucl . El . ) and consequently it is not expreffible by any rational Number . Alfo the Cube - Root of b2 can be only writ thus b3 ( = b3 ) thus b . & c . 2. But altho these Surd - Roots ( when truly ...
... also a Fraction , ( by the 16. 8. Eucl . El . ) and consequently it is not expreffible by any rational Number . Alfo the Cube - Root of b2 can be only writ thus b3 ( = b3 ) thus b . & c . 2. But altho these Surd - Roots ( when truly ...
Άλλες εκδόσεις - Προβολή όλων
A Treatise of Algebra: In Two Books; The First Treating of the Arithmetical ... Philip Ronayne Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ... PHILIP. RONAYNE Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
Æquation alfo alſo Angle Anſwer Axiom Bafe becauſe Binomial Cafe Canon Chap Co-fine common confequently conjoin'd Cube Cubick Demonftration Denominator Divided Divifion Divifor equal Equation Eucl Example faid fame fecond Term feven fhall fide figurate Number fince firft Term firſt fome foregoing Fraction fuch fuppofe given Number greater greateſt Hence indefinitely Intereft laft leaft Leffer Series lefs Legs Lemma Logarithm Meaſure muft Multiply muſt Number of Alternations number of Terms oppofite Power Product propos'd Quadratick Quantities Queftion Quotient Rank Rational Theorem reduc'd Refidual Refolvend refpectively Remainder required to find ſaid Scholium Sine Solution Spheric Triangle Square fought Square Root Subftract Surds thefe Theorem theſe thofe Triangle Uncia univerfal unknown Root Value wherefore whofe
Δημοφιλή αποσπάσματα
Σελίδα 290 - 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.
Σελίδα 31 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Σελίδα 312 - In spherical triangles, whether right angled or oblique angled, the sines of the sides are proportional to the sines of the angles opposite to them.
Σελίδα 258 - 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, etc.
Σελίδα 289 - In any triangle, the sides are proportional to the sines of the opposite angles, ie. t abc sin A sin B sin C...
Σελίδα 200 - JJ/xJV; hence, The sum of the logarithms of any two numbers is equal to the logarithm of their product.
Σελίδα 263 - 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.
Σελίδα 97 - Note. — In any series of numbers in arithmetical progression, the sum of the two extremes is equal to the sum of any two terms equally distant from them; as in the latter of the above series 6 + 1=4+3, and =5+2.
Σελίδα 290 - FA : FG ; that is in Words, half the Sum of the Legs is to half their Difference, as the Tangent of half the Sum of the oppofite Angles is to the Tangent of half their Difference : But Wholes are as their Halves ; wherefore the Sum of the Legs is...
Σελίδα 32 - Then multiply the denominator of the dividend by the numerator of the divifor, and their produft Jhall give the denominator.