A mathematical treatise: containing a system of conic-sections; with the doctrine of fluxions and fluents, applied to various subjects; viz. to the finding the maximums and minimums of quantities; radii of evolution, refraction, reflection; superficial and solid contents of curvilinear figures; rectification of curve-lines; centers of gravity, oscillation and percussion. As also to the resolution of a select collection of the most useful, and many new, physicomathematical problems
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absciss AP asymptote axis become bisect Cafe call'd Center of gravity Circle circular arch circular Sectors circular velocity circumference Conic-Section Consequently Corollary Cycloid describe the Curve directrix distance required draw the lines Ellipsis or Hyperbola equal Equation EXAMPLE fame manner find the Expression fluent force give given angle given in position given points GMTV Hyperbolical Sector Hyperbolical Space infinite intersection likewise line drawn thro lipsis Logarithm meet the Curve Momentums multiplied ordinates Parabola Parallelogram particle pass thro perpendicular plane Point F points of contact PROBLEM produced quantity radii Radius of Evolution ratio Rectangle right angles right line rotation Scholium semi-ordinate PM sides similar triangles Solid Space AMP Square Subtangent supposed Surface described tangent TEnce terminated THEOREM trapezium vertex Voussoir weight whence
Page 8 - ... conversely, if two triangles have two sides of one equal, respectively, to two sides of the other, but the third side of the first greater than the third side of the second, the angle opposite the third side of the first is. greater than the angle opposite the third side of the second. 5. Theorem. The sum of two lines drawn from any point to the extremities of a straight line is greater than the sum of two lines similarly drawn but included by them. 6. Theorem. Through any point one perpendicular...
Page 28 - Diameter ; the line joining the points of contacT: of two tangents, drawn from any point of the line DT to the Seclion, will always pafs thro...
Page 94 - Cauftick; but it may be proved as already, that the Difference between the incident Rays, is always to the Difference of the refracted Rays plus the part of the Cauftick between thofe Rays, as m to n.
Page 78 - I :mym—l::y : myym—* that is, unity is to mym—ly or_y is to myy — ', as the fluxion or velocity with which y is generated, is to the fluxion, or contemporary velocity with which y"> is generated, and fo for the reft.
Page 162 - Piece of ivood placed horizontally, and fup*-* ported by the pieces AB, AB, 'which make a given angle ABC with the former ; it is required to...
Page 66 - From whence it appears, that each of the oppofite Sections are infinite,, and do not return into themfelves. COROLLARY IIL 146. yi LL the Sides produced, will meet the Parabolical _£~JL Plane, except the Side KD, which is drawn from/ the vertex K thro...
Page 144 - Ofcillation, is a point in the axis of a compound Pendulum, whofe diftance from the point of Sufpenfion is equal to the lengths of a fimple Pendulum, Ifbcronous to the former.
Page 1 - RANT that two infinite quantities, differing from each other by a finite quantity, may be efteemed HM^JiaP equal. l&gfflgS This Poftulatum is here of ufe only to (hew the <5|7<SwK connection of the Conic-Sections...