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 xi
... Quadrilateral 223 Solid angles 64 Polygons , rectilinear and polyhedral 227 Analogies , etc. 67 Theorems of Pappus and Desargues 229 Harmonical sections of an arc . ........................ . 76 Conical transversals 232 Spherical ...
... Quadrilateral 223 Solid angles 64 Polygons , rectilinear and polyhedral 227 Analogies , etc. 67 Theorems of Pappus and Desargues 229 Harmonical sections of an arc . ........................ . 76 Conical transversals 232 Spherical ...
Página 21
... quadrilaterals , F , pentagons , and so on . Then 3 ... 2F2F , 2F1 + 2F , + 2E3F , 4F , + 5F , + .... - Whence , these being substituted in 2E 2F 2 ( S- reduced to the appropriate form , we get 2 ) and the result + - — — 4 F , F , + F ...
... quadrilaterals , F , pentagons , and so on . Then 3 ... 2F2F , 2F1 + 2F , + 2E3F , 4F , + 5F , + .... - Whence , these being substituted in 2E 2F 2 ( S- reduced to the appropriate form , we get 2 ) and the result + - — — 4 F , F , + F ...
Página 23
... quadrilateral be inscribed in a less circle of the sphere , the sum of one pair of opposite angles will be equal to the sum of the other pair . 9. If a great - circle quadrilateral be described about a less circle of the sphere , and ...
... quadrilateral be inscribed in a less circle of the sphere , the sum of one pair of opposite angles will be equal to the sum of the other pair . 9. If a great - circle quadrilateral be described about a less circle of the sphere , and ...
Página 65
... quadrilateral angle . Second . Bisect either diagonal of the base , and draw any plane to pass through the point of bisection and the vertex of the pyramid ; such plane , if it do not coincide with the former , will divide the quadrilateral ...
... quadrilateral angle . Second . Bisect either diagonal of the base , and draw any plane to pass through the point of bisection and the vertex of the pyramid ; such plane , if it do not coincide with the former , will divide the quadrilateral ...
Página 69
... quadrilateral inscribed in a circle , we shall have sina 2 sinc , = where a is the diagonal , and c one of the equal sides . Corollary 3 . If there be a spherical parallelogram , that is , a quadrilateral whose opposite sides are equal ...
... quadrilateral inscribed in a circle , we shall have sina 2 sinc , = where a is the diagonal , and c one of the equal sides . Corollary 3 . If there be a spherical parallelogram , that is , a quadrilateral whose opposite sides are equal ...
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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.