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
... diameter of the sphere is any line drawn through the centre , and terminated both ways by the surface . 4. A diametral plane is any plane drawn through the centre ; and its inter- section with the surface of the sphere is a great circle ...
... diameter of the sphere is any line drawn through the centre , and terminated both ways by the surface . 4. A diametral plane is any plane drawn through the centre ; and its inter- section with the surface of the sphere is a great circle ...
Página 3
... diameter of each circle . The arcs BDF , BAF , BCF , BEF are , therefore , semi - circles ; or the two circles mutually bisect each other at B and F , their intersections on the surface of the sphere . PROP . II . THEOREM . If a plane ...
... diameter of each circle . The arcs BDF , BAF , BCF , BEF are , therefore , semi - circles ; or the two circles mutually bisect each other at B and F , their intersections on the surface of the sphere . PROP . II . THEOREM . If a plane ...
Página 4
... diameter of the sphere at its extremities are parallel tangent planes . Corollary 2 . If tangent planes be drawn to a sphere at the opposite extremities of a diame- ter , they will be parallel . Corollary 3 . Parallel tangent planes ...
... diameter of the sphere at its extremities are parallel tangent planes . Corollary 2 . If tangent planes be drawn to a sphere at the opposite extremities of a diame- ter , they will be parallel . Corollary 3 . Parallel tangent planes ...
Página 18
... diameter AA ' of the sphere , cut the surface in ACA ' , ABA ' , ADA ' . Then the lune contained by ACA ' , ABA ' , will be to that contained by ABA ' , ADA ' , as the angle CAB to the angle BAD . GFE CBD H K For , let the plane CBD ...
... diameter AA ' of the sphere , cut the surface in ACA ' , ABA ' , ADA ' . Then the lune contained by ACA ' , ABA ' , will be to that contained by ABA ' , ADA ' , as the angle CAB to the angle BAD . GFE CBD H K For , let the plane CBD ...
Página 30
... diameter through E , we shall have tan2 EF = tan EB tan ED . 10. If from the extremities of the diameter AB of a less circle arcs be drawn to any point F in the circumference , then , sin2 BF + sin2 FD = sin2 3 BD . 11. If from any ...
... diameter through E , we shall have tan2 EF = tan EB tan ED . 10. If from the extremities of the diameter AB of a less circle arcs be drawn to any point F in the circumference , then , sin2 BF + sin2 FD = sin2 3 BD . 11. If from any ...
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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.