Syntagma Mathesios: Containing the Resolution of Equations with a New Way of Solving Cubic and Biquadratic Equations Analytically and Geometrically : Also the Universal Method of Converging Series, After an Easy and Expeditious Manner Wherein Also are Treated the Series for Trigonometrical Operations ; Some New Useful Properties of Conics, Centre of Oscillation, the Direct and Inverse Method of the Laws of Centripetal Forces, a Variety of Exponential Equations, with the Investigation of Several Other Abstruse Problems : To All which Prefixed an Essay on the MathematicsJ. Fuller, 1745 - 312 σελίδες |
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Σελίδα 43
... Equa- tion is most commonly render'd much more fimple , and may be fometimes depreffed to a lower Degree . For thus x4qxx -- s is to be reckon'd an Equation of the fe- cond Degree , because it may be refolved into two Equa- tions of the ...
... Equa- tion is most commonly render'd much more fimple , and may be fometimes depreffed to a lower Degree . For thus x4qxx -- s is to be reckon'd an Equation of the fe- cond Degree , because it may be refolved into two Equa- tions of the ...
Σελίδα 74
... Equa- tion you have ( first multiplying by y3 , and dividing by x3 ) y6 + y ++ y2 + 1 = —— 33 . Confequently you will have the Value of y . x3 EXAMPLE 18 . 3 % Suppose 2x2 + 33113 + 6x13 = a . The fame Equation may be fet thus , 21 = 3 ...
... Equa- tion you have ( first multiplying by y3 , and dividing by x3 ) y6 + y ++ y2 + 1 = —— 33 . Confequently you will have the Value of y . x3 EXAMPLE 18 . 3 % Suppose 2x2 + 33113 + 6x13 = a . The fame Equation may be fet thus , 21 = 3 ...
Σελίδα 80
... Equa- tion is 1 & 2 Now for 23 + 3 put put , and for a6 c6 rt put > SS rt 2 x and 3 4 and 34 3 4 5 x = S rt SS 1 x = 1 x + 1 SS SS s2y2x = s2rtx = st / p 72x7tx = s2p ssp and Here 81 Here you fee how in Equations , where Subftitution [ 80 ]
... Equa- tion is 1 & 2 Now for 23 + 3 put put , and for a6 c6 rt put > SS rt 2 x and 3 4 and 34 3 4 5 x = S rt SS 1 x = 1 x + 1 SS SS s2y2x = s2rtx = st / p 72x7tx = s2p ssp and Here 81 Here you fee how in Equations , where Subftitution [ 80 ]
Σελίδα 83
... Equa- tion and Vy - the Numerator and De- nominator are alike , and confequently deftroy each other , whence we have the fecond Step , and confequently free from Surds . EXAMPLE . a Equation Vita b √i + a2 — a2 — x2 X2 ax2 I X x2 2 22 ...
... Equa- tion and Vy - the Numerator and De- nominator are alike , and confequently deftroy each other , whence we have the fecond Step , and confequently free from Surds . EXAMPLE . a Equation Vita b √i + a2 — a2 — x2 X2 ax2 I X x2 2 22 ...
Σελίδα 84
... 3xx ) , involve this Equa- tion , and it becomes 4b4x6 = 64s2 - † 3b4s2x2 , or x6 - I s2 , and now put z = x2 , then z3 3 s2x2 = 4 4 I $ 2 % = s2 . in its lowest Terms , 4 . 1 - 3 4 OPERATION , OPERATION . b2x I - 2xx√ -xx ) I + [ 84 ]
... 3xx ) , involve this Equa- tion , and it becomes 4b4x6 = 64s2 - † 3b4s2x2 , or x6 - I s2 , and now put z = x2 , then z3 3 s2x2 = 4 4 I $ 2 % = s2 . in its lowest Terms , 4 . 1 - 3 4 OPERATION , OPERATION . b2x I - 2xx√ -xx ) I + [ 84 ]
Συχνά εμφανιζόμενοι όροι και φράσεις
affuming alfo Angle Area Axis becauſe Biquadratic Equations Body c²x² Cafe Centre Centripetal Force Circle Co-efficients Cofine Confequently Converging Series COROLLARY Cube Cubic Equation Curve defcribed demonftrated Diſtance Divifor eafily Ellipfis Equa equal Equation EXAMPLE expreffed fame fecond fhall fhew fhould firft firſt Fluent Fluxion fmall fome fought fubftituted fuch Geometry given greateſt Hyperbola infinite interfecting laft laſt Latus Rectum leaft leffer lefs likewife Logarithm m+n=x Mathematics Meaſure Method moſt multiplied muſt neceffary Number Obfervations Ordinate Parabola Perpendicular Pleaſure Point propofed Propofition Quotient Radius Ratio Reaſon refpectively right Line Root SCHOLIUM ſhall Sine Square Suppofe Surd Table of Powers Tangent Terms thefe themſelves Theorem theſe thofe thoſe tion Tranfpofition Triangle underſtand Univerfal unknown Quantity uſeful Value Velocity whence wherefore whofe whoſe
Δημοφιλή αποσπάσματα
Σελίδα 5 - By giving us a clear and extensive knowledge of the system of the world, which, as it creates in us the most profound reverence of the Almighty and wise Creator, so it frees us from the mean and narrow thoughts which ignorance and superstition are apt to beget.
Σελίδα 26 - I dare not affirm that it has attained its utmoft Perfection. And tho* where the Ground is regular, it admits but of fmall Variety, the Meafures being pretty well determined by Geometry and Experience, yet where the Ground is made up of natural Strengths and Weakneffes, it affords fbme Scope for thinking and Contrivance.
Σελίδα 3 - This they do by entertaining it with a great variety of truths, which are delightful and evident, but not obvious. Truth is the same thing to the understanding as music to the ear and beauty to the eye.
Σελίδα 6 - ... of imagination, and purge the mind from error and prejudice. Vice is error, confusion, and false reasoning ; and all truth is more or less opposite to it. Besides, mathematical studies may serve for a pleasant entertainment for those hours which young men are apt to throw away upon their vices ; the delightfulness of them being such as to make solitude not only easy, but desirable.
Σελίδα 6 - I proceed now to fhew their vaft Extent and Ufefulnefs in other Parts of Knowledge. And here it might fuffice to tell you, that Mathematics is the Science of Quantity, or the Art of Reafoning about Things, that are capable of...
Σελίδα 22 - Impediment is too great for them ; or Hydraulic Engines for raifing of Water, ferving for great Ufe and Comfort to Mankind, where they have no other Way to be fupply'd readily with that...
Σελίδα 6 - Suggeftion, as if Mathematics were an Enemy to Religion, which is a Scandal thrown both on the one and the other ; for Truth can never be an Enemy to true Religion, which appears always to the beft Advantage, when tt is moft examined.
Σελίδα 33 - Man of good fenfe and application is the Perfon, that is by nature fitted for them : efpecially if he begins betimes : And if his circumftances have been fuch, that this did not happen, by prudent direction the defect may be fupply'd as much as in any Art whatfoever.
Σελίδα 10 - Newton fhall be pleas'd to gratify the World with his Book of Light and Colours. . : , ' : The Fluids which involve our Earth , viz. Air and Water , are the next great and confpicuous Bodies^ that Nature. prefents to our view : And I think we know little of either, but what is owing to Mechanicis and Geometry.
Σελίδα 17 - Aretinus, by inventing the Temperament, making the Fifth falfe by a certain determined Quantity, taught us to tune our Organs, and intermix all the three kinds of the Ancients ; to which we owe all the regular and noble Harmony of our modern Mufic.