A Course of Mathematics: In Two Volumes. Composed for the Use of the Royal Military Academy, Volumen2Longman, Orme & Company, 1843 |
Dentro del libro
Resultados 1-5 de 97
Página xi
... Third case 60 Co - polar and co - axial triangles 221 Areas of spherical triangles 62 Quadrilateral 223 Solid angles 64 Polygons , rectilinear and polyhedral 227 Analogies , etc. 67 Theorems of Pappus and Desargues 229 Harmonical ...
... Third case 60 Co - polar and co - axial triangles 221 Areas of spherical triangles 62 Quadrilateral 223 Solid angles 64 Polygons , rectilinear and polyhedral 227 Analogies , etc. 67 Theorems of Pappus and Desargues 229 Harmonical ...
Página 7
... third ; and ABC ' , abc ' , are the fourth . For , by the hypothesis , the first pair ABC , abc , are mutual polars ; and hence B is the pole of ac , that is of ac ' ; A is the pole of bc , that is of be ' ; and since C is the pole of ...
... third ; and ABC ' , abc ' , are the fourth . For , by the hypothesis , the first pair ABC , abc , are mutual polars ; and hence B is the pole of ac , that is of ac ' ; A is the pole of bc , that is of be ' ; and since C is the pole of ...
Página 10
... third , and the difference of any two is less than the third . FOR , let O be the centre of the sphere upon which the spherical triangle ABC is described , and join OA , OB , OC . Then AOB , BOC , COA , are the plane angles which ...
... third , and the difference of any two is less than the third . FOR , let O be the centre of the sphere upon which the spherical triangle ABC is described , and join OA , OB , OC . Then AOB , BOC , COA , are the plane angles which ...
Página 16
... third interior one ; and the point of section is the pole , or spherical centre , of the corresponding inscribed triangle . LET O be the point of section of the arcs BO , CO , which bisect the interior angles B and C , and join OA ...
... third interior one ; and the point of section is the pole , or spherical centre , of the corresponding inscribed triangle . LET O be the point of section of the arcs BO , CO , which bisect the interior angles B and C , and join OA ...
Página 32
... C ) + sin ( II — B ) sin ( IIC ) cos ( π — a ) - by expanding which , and changing all the signs , we get - - cos Acos B cos C + sin B sin C cos a . Multiply the third equation of system ( 4 ) by 32 SPHERICAL TRIGONOMETRY .
... C ) + sin ( II — B ) sin ( IIC ) cos ( π — a ) - by expanding which , and changing all the signs , we get - - cos Acos B cos C + sin B sin C cos a . Multiply the third equation of system ( 4 ) by 32 SPHERICAL TRIGONOMETRY .
Otras ediciones - Ver todas
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.