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 2
... intersection of the surface of the sphere by an excentric plane is called a less circle of the sphere . 6. A tangent ... intersect each other , they divide the surface into four portions , called spherical lunes ; and the enclosed ...
... intersection of the surface of the sphere by an excentric plane is called a less circle of the sphere . 6. A tangent ... intersect each other , they divide the surface into four portions , called spherical lunes ; and the enclosed ...
Página 4
... intersection ; then EBG is equal to the spherical angle formed by the circles BAD , BMD . For the tangents BE , BG to the circles are both perpen- dicular to their common diameter : and hence ( vol . i . p . 347 , def . 4 , ) the angle ...
... intersection ; then EBG is equal to the spherical angle formed by the circles BAD , BMD . For the tangents BE , BG to the circles are both perpen- dicular to their common diameter : and hence ( vol . i . p . 347 , def . 4 , ) the angle ...
Página 9
... intersection K is the pole of BC ; and in the same way it may be proved that Q is the pole of AC . Again , since B is the pole of HGM , BG is a quadrant ; and for the same reason AG is a quadrant : hence G is the pole of AB . Lastly ...
... intersection K is the pole of BC ; and in the same way it may be proved that Q is the pole of AC . Again , since B is the pole of HGM , BG is a quadrant ; and for the same reason AG is a quadrant : hence G is the pole of AB . Lastly ...
Página 14
... intersection , and hence no solution at all ; and when a = CD there will be one solution , the triangle being right ... intersections b and b ' ( pr . xviii . cor . 4 ) ; and hence two triangles AbC and Ab'C , which have all the data ...
... intersection , and hence no solution at all ; and when a = CD there will be one solution , the triangle being right ... intersections b and b ' ( pr . xviii . cor . 4 ) ; and hence two triangles AbC and Ab'C , which have all the data ...
Página 23
... intersection will always be in the same great circle , which is perpendicular to the arc drawn from the given point to the centre of the given circle . RIGHT - ANGLED SPHERICAL TRIANGLES . PROP . I. In GEOMETRICAL THEOREMS . 23.
... intersection will always be in the same great circle , which is perpendicular to the arc drawn from the given point to the centre of the given circle . RIGHT - ANGLED SPHERICAL TRIANGLES . PROP . I. In GEOMETRICAL THEOREMS . 23.
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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.