The MathematicianJ. Wilcox, 1751 - 399 σελίδες |
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Σελίδα 5
... Arch of a Curve and a right Line , which he did by demonftrating that the Seg- ment of a Parabola is to its infcribed Triangle , as 4 : 3 . Cotemporary with him was Conon ; and at no great Distance of Time was Apollonius , of Perga ...
... Arch of a Curve and a right Line , which he did by demonftrating that the Seg- ment of a Parabola is to its infcribed Triangle , as 4 : 3 . Cotemporary with him was Conon ; and at no great Distance of Time was Apollonius , of Perga ...
Σελίδα 8
... Arches , which the Sides of the Polygon fubtend , could become lefs than any Quantity that could be affigned ; and that all this while the fimilar Polygons obferved the fame conftant invariable Proportions to each other , viz . that of ...
... Arches , which the Sides of the Polygon fubtend , could become lefs than any Quantity that could be affigned ; and that all this while the fimilar Polygons obferved the fame conftant invariable Proportions to each other , viz . that of ...
Σελίδα 53
... Arch . We must not omit to obferve a very remarkable Conclufion that Dr. Wallis obtained in his Arith . Inf . by his gradual Method of Induction . He confidered those Progreffions as confifting of an in- finite Number of Terms ; and ...
... Arch . We must not omit to obferve a very remarkable Conclufion that Dr. Wallis obtained in his Arith . Inf . by his gradual Method of Induction . He confidered those Progreffions as confifting of an in- finite Number of Terms ; and ...
Σελίδα 97
... Arches FH ( 50 ° 45 ′ 44 ′′ ) and GO ( 14 ° 52 ′ 2 ′′ ) become known : Thus far Mr. Turner : But in order to obtain the Declination and Latitude from thence , it is mani- feft that the Arch HF - EF - GO = EF ; and confequently therefore ...
... Arches FH ( 50 ° 45 ′ 44 ′′ ) and GO ( 14 ° 52 ′ 2 ′′ ) become known : Thus far Mr. Turner : But in order to obtain the Declination and Latitude from thence , it is mani- feft that the Arch HF - EF - GO = EF ; and confequently therefore ...
Σελίδα 101
... Arches IA , IB as well as the Angles AEI , and BEI are equal . Q. E. D. Method of Calculation . As the Line bifecting the vertical Angle , is to the Perpendicular , fo is Radius , to the Cofine of half the Difference of the Angles at ...
... Arches IA , IB as well as the Angles AEI , and BEI are equal . Q. E. D. Method of Calculation . As the Line bifecting the vertical Angle , is to the Perpendicular , fo is Radius , to the Cofine of half the Difference of the Angles at ...
Συχνά εμφανιζόμενοι όροι και φράσεις
Abfciffa Abfcifs affigned Affymptotes alfo alſo Anfwered by John Arch Bafe Baſe becauſe bifecting Cafe Center Circle circumfcribing Cofine confequently Curve defcribed DEMONSTRATION determine Diameter Difference Diſtance draw Ellipfe equal Equation expreffed Expreffion faid fame fecond fhall fhew fimilar Triangles fince finite firft firſt flowing Quantities Fluent Fluxions fome fuch fuppofed Geometry given greateſt Hyperbola increaſe infcribed infinite infinite Series Interfection John Turner laft leffer lefs Magnitude Meaſure Method Method of Fluxions Motion muſt Number Ordinate paffing Parabola parallel Parallelogram Parameter perpendicular Pofition Point of Contact PROBLEM Progreffion Prop propofed Proportion Q. E. D. PROPOSITION Radius Reaſoning Rectangle refpectively reprefent right Angle right Line Semi-diameter Sides Sine Sir Ifaac Space Square Subtangent Tangent thefe theſe thofe thoſe thro tion tranfverfe Axe Trapezium ultimate Ratio Velocity Vertex whence whofe
Δημοφιλή αποσπάσματα
Σελίδα 157 - 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 193 - Velocity with which they increase and are generated; I sought a Method of determining Quantities from the Velocities of the Motions or Increments, with which they are generated; and calling these Velocities of the Motions or Increments Fluxions, and the generated Quantities Fluents, I fell by degrees upon the Method of Fluxions, which I have made use of here in the Quadrature of Curves, in the Years 1665 and 1666.
Σελίδα 6 - They found, that similar triangles are to each other in the duplicate ratio of their homologous sides; and, by resolving similar polygons into similar triangles, the same proposition was extended to these polygons also.
Σελίδα 13 - ... all their theorems of this kind. It is often said, that curve lines have been considered by them as polygons of an infinite number of sides. But this principle no where appears in their writings. We never find them resolving any figure, or solid, into infinitely small elements.
Σελίδα 57 - Whatfoever politive ideas we have in our minds of any fpace, duration, or number, let them be ever fo great, they are ftill finite ; but when we fuppofe an inexhauftible remainder, from which we remove all bounds, and wherein we allow the mind an endlefs...
Σελίδα 205 - ... time approach to each other within less than any given difference, become ultimately equal. If you deny it, let them be ultimately unequal, and let their ultimate difference be D, then they cannot approach nearer to equality than quantities having a difference D: which is against the hypothesis.
Σελίδα 193 - I consider mathematical quantities in this place not as consisting of very small parts, but as described by a continued motion. Lines are described, and therefore generated not by the apposition of parts, but by the continued motion of points ; superficies by the motion of lines ; solids by the motion of superficies ; angles by the rotation of the sides ; portions of time by a continual flux ; and so in other quantities. These geneses really take place in the nature of things, and are daily seen...
Σελίδα 65 - ... of the simple addition of rising Moments, or of the continual flux of one Moment, and for that reason ascribe only length to it, and determine its quantity by the length of the line passed over : As a line, I say, is looked upon to be the trace of a point moving forward, being in some sort divisible by a point, and may be divided by Motion one way, viz. as to length ; so Time may be conceived as the trace of a Moment continually flowing, having some kind of divisibility from an Instant, and from...
Σελίδα 192 - ... flowing quantities." For example: I don't here consider Mathematical Quantities as composed of Parts extremely small, but as generated by a continual motion. Lines are described, and by describing are generated, not by any apposition of Parts, but by a continual motion of Points. Surfaces are generated by the motion of Lines, Solids by the motion of Surfaces, Angles by the Rotation of their Legs, Time by a continual flux...
Σελίδα 6 - ... objections that have been made to it. But, before we proceed, it may be of use to consider the...