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 15
... last Contempt for thofe Gen- tlemen , that pretend to explain how the Earth was framed , and yet can hardly Measure an Acre of Ground upon the Surface of it . And as the Philofopher fpeaks , Qui repente pedibus illotis ad Philofophos ...
... last Contempt for thofe Gen- tlemen , that pretend to explain how the Earth was framed , and yet can hardly Measure an Acre of Ground upon the Surface of it . And as the Philofopher fpeaks , Qui repente pedibus illotis ad Philofophos ...
Σελίδα 41
... or Compofition : For in this Analytical Method the Propofition is propofed as already known , granted or done ; and then the Confequences thence deducible are examined , G examined , till at last we come to fome known [ 41 ]
... or Compofition : For in this Analytical Method the Propofition is propofed as already known , granted or done ; and then the Confequences thence deducible are examined , G examined , till at last we come to fome known [ 41 ]
Σελίδα 42
... last we come to fome known Truth or Falfhood , or Impoffibility , whereof that which was pro- pofed is a neceffary Confequence , and from thence justly conclude the Truth or Impoffibility of the Propofition ; which , if true , may then ...
... last we come to fome known Truth or Falfhood , or Impoffibility , whereof that which was pro- pofed is a neceffary Confequence , and from thence justly conclude the Truth or Impoffibility of the Propofition ; which , if true , may then ...
Σελίδα 93
... last Divifor ( by Reason of un- like Signs ) 10800 1440 9360 ) 88000 ( 9n more nearly . Confequently = m + n = 69. 401 . Here the Learner may fee , That after I had noted down my Equation for Con- verging Series , firft I confider well ...
... last Divifor ( by Reason of un- like Signs ) 10800 1440 9360 ) 88000 ( 9n more nearly . Confequently = m + n = 69. 401 . Here the Learner may fee , That after I had noted down my Equation for Con- verging Series , firft I confider well ...
Σελίδα 127
... Then our Univerfal Theorem will be G - m3 + 180m2 - 10800m 3m2 + 3mn - 360m - 180n + 10800 * Hence the Value of m + nx = 34.7 . EXAMPLE 3 . Given ax3 - bx2 - cx = N. W. W. R. Then Then by Divifion and Subftitution , as the two last [ 127 ]
... Then our Univerfal Theorem will be G - m3 + 180m2 - 10800m 3m2 + 3mn - 360m - 180n + 10800 * Hence the Value of m + nx = 34.7 . EXAMPLE 3 . Given ax3 - bx2 - cx = N. W. W. R. Then Then by Divifion and Subftitution , as the two last [ 127 ]
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.