A Course of Mathematics: In Two Volumes. Composed for the Use of the Royal Military Academy, Volumen2Longman, Orme & Company, 1843 |
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Página xii
... axes , etc. of circles Exercises on the circle 285 Rationalisation 461 288 Correction of integrals 468 290 Integration by parts 471 Binomial surds . 472 . Trinomials 481 Logarithmic functions 483 Exponentials 485 Trigonometrical ...
... axes , etc. of circles Exercises on the circle 285 Rationalisation 461 288 Correction of integrals 468 290 Integration by parts 471 Binomial surds . 472 . Trinomials 481 Logarithmic functions 483 Exponentials 485 Trigonometrical ...
Página 74
... axes will pass through the same point 0 ; the tangents from O to the three circles will be equal ; and the circle described from centre O with radius equal to one of the equal tangents will cut the other three at right angles . 1. Let ...
... axes will pass through the same point 0 ; the tangents from O to the three circles will be equal ; and the circle described from centre O with radius equal to one of the equal tangents will cut the other three at right angles . 1. Let ...
Página 75
... axes of ( A ) , ( B ) , ( C ) taken two and two ; and let ( D ) be any other circle on the sphere , the radical axes of ( D ) with each of the other three taken separately will meet two and two in the first three ; viz . those ( A ) ...
... axes of ( A ) , ( B ) , ( C ) taken two and two ; and let ( D ) be any other circle on the sphere , the radical axes of ( D ) with each of the other three taken separately will meet two and two in the first three ; viz . those ( A ) ...
Página 105
... axes ; take any point I in one of the lines of contact , and draw the per- pendiculars IH , IK cutting the axes in a and B , and being themselves conse- quently bisected in those points . Then if the cones whose axial sections are HCI ...
... axes ; take any point I in one of the lines of contact , and draw the per- pendiculars IH , IK cutting the axes in a and B , and being themselves conse- quently bisected in those points . Then if the cones whose axial sections are HCI ...
Página 106
... axes aC , CA to be in the same plane and the sectional plane parallel to it . The conjugate hyperbolas are then equal in all respects ; and in this case , either of them is called a rectangular hyperbola , or an equilateral hyperbola ...
... axes aC , CA to be in the same plane and the sectional plane parallel to it . The conjugate hyperbolas are then equal in all respects ; and in this case , either of them is called a rectangular hyperbola , or an equilateral hyperbola ...
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A Course of Mathematics ...: Composed for the Use of the Royal Military Academy Charles Hutton,Olinthus Gregory Sin vista previa disponible - 2016 |
Términos y frases comunes
a₁ abscisses asymptotes axes axis B₁ bisected Ca² centre circle co-ordinates cone conic section conoïd Corollary corresponding cosec curvature curve cx² denoted differential co-efficients directrix distance draw drawn ellipse equal equation expression focus function given line hence hyperbola inscribed integral intersection lemniscate of Bernoulli loge meet ordinate p₁ parabola parallel pass perpendicular plane points of contact polar pole polygon preceding PROP proposition quadrilateral r₁ radius ratio rectangle rectangular referred respectively right angles right ascension Scholium segments sides sin² solid angle sphere spherical triangle straight line subtangent tangent Taylor's theorem theorem tractory transverse transverse plane triangle ABC values variable vertex whence Wherefore x₁ y₁
Pasajes populares
Página 2 - A diameter is any straight line drawn through the centre and terminated both ways by the surface.
Página 10 - Any two sides of a spherical triangle are together greater than the third side.
Página 14 - The problem is impossible when one of the given sides is equal to or greater than the sum of the other two (I. 66). F C" E PROPOSITION XXXV.— PROBLEM.
Página 311 - ... the points of intersection of the three pairs of opposite sides, of a hexagon inscribed in a conic, lie in one straight line.
Página 34 - Law of cosines for sides: cos a = cos b cos с + sin 6 sin с cos A cos b = cos a cos с + sin a sin с cos ß cos с = cos a cos...
Página 151 - If a Tangent and Ordinate be drawn from any Point in the Curve, meeting the Transverse Axis ; the Semi-transverse will be a Mean Proportional between the Distances of the said Two Intersections from the Centre. That is, •€A is a mean proportional between CD and CT ; or CD, CA, CT, are continued proportionals.
Página 292 - If two circles touch each other, the straight line joining their centres passes through the point of contact.
Página 105 - MF+MF' is equal to a given line. II. The straight line drawn through the foci, and terminated by the curve, is called the transverse or major axis. The middle of that part of the transverse axis which lies between the foci, is called the centre of the ellipse. The straight line drawn through the centre, at right angles to the transverse axis, and terminated by the curve, is called the conjugate or minor axis. Thus, if the straight line joining F and F...
Página 85 - AMPLITUDE, is an arc of the horizon intercepted between the east or west point, and the centre of the sun, or star, at its rising or setting.