## 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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### Common terms and phrases

abſciſs alſo aſymptote baſe becauſe biſe&ts Caſe Center of gravity circular arch circumference Conic-Sečtion Conſequently conſtant correſpondent Curve deſcribed diameter Aa diſtance E X A M P L E Ellipſis equal Equation expreſs F1 G fimilar triangles fince find the Expreſſion firſt axis given in poſition given points Hyperbola increaſes inſtead interſe&tion laſt likewiſe line drawn thro Logarithm multiplied oppoſite P R O B L E M Parabola parallel particle paſs paſſing thro perpendicular plane point G preſſes produćt R O L L A R Y reſiſtance reſpect reſt right angles right line ſaid ſame manner ſecond Sečtion Sečtor ſhall ſhews ſides ſince ſpace ſquare ſtrike ſubſtituting ſuch ſum ſuppoſed T H E O R E M tangent theſe thoſe trapezium uſe vertex whoſe fluent whoſe fluxion whoſe radius

### Popular passages

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 - P ; and the line joining the points of contact of two tangents, drawn from any point of the line P t, will always pafs thro

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 93 - 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 75 - 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 160 - 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 142 - 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...

Page 93 - F removes at an infinite diftance from the Curve AM, that is, if the incident Rays FA, FM, become parallel; we mall ftill have LH=AH— ML— J?