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 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 16.
Σελίδα 94
... Second Operation , ) the Imperfection being only in the laft Figure of the Root , fo increased , which often proves too large , and therefore confequently the next converging Number n will have the Negative Sign - · Alfo if there happen ...
... Second Operation , ) the Imperfection being only in the laft Figure of the Root , fo increased , which often proves too large , and therefore confequently the next converging Number n will have the Negative Sign - · Alfo if there happen ...
Σελίδα 120
... second Value of n to have a Negative Sign before it , fhews , that I affumed m too much , and therefore must deduct n from m ; as man = x = 25.7635 . ( See Form 16th . ) Q. E. I. of Of the Square Cubed , or Cube Squared , the [ 120 ]
... second Value of n to have a Negative Sign before it , fhews , that I affumed m too much , and therefore must deduct n from m ; as man = x = 25.7635 . ( See Form 16th . ) Q. E. I. of Of the Square Cubed , or Cube Squared , the [ 120 ]
Σελίδα 124
... second is the Exponent of the first , and of the third is the Exponent of m in the fecond Term , multiplied by the affix'd Uncia , and divided by 2 = 15 , and of the third is the Exponent of m in the third Term , multiplied by the ...
... second is the Exponent of the first , and of the third is the Exponent of m in the fecond Term , multiplied by the affix'd Uncia , and divided by 2 = 15 , and of the third is the Exponent of m in the third Term , multiplied by the ...
Σελίδα 132
... always n , the Expo- nent of the highest Power . 13 1 COROLLARY 22 2 . That the Root or Side of n , the unknown Quantity , is always multiplied into the Second Term of the known . Now Now from the Latter , it is evident we are [ 132 ]
... always n , the Expo- nent of the highest Power . 13 1 COROLLARY 22 2 . That the Root or Side of n , the unknown Quantity , is always multiplied into the Second Term of the known . Now Now from the Latter , it is evident we are [ 132 ]
Σελίδα 135
... Second General Theorem . Tm the 2d . Then [ T = m the 2d . Then T = m the 3d . Then | Tm the 3d . Then Tm the 4th . Then | Tm the 4th . Then Tm the 5th , & c . Tm the 5th . & c . Some of which true Values of m will terminate in the true ...
... Second General Theorem . Tm the 2d . Then [ T = m the 2d . Then T = m the 3d . Then | Tm the 3d . Then Tm the 4th . Then | Tm the 4th . Then Tm the 5th , & c . Tm the 5th . & c . Some of which true Values of m will terminate in the true ...
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.