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解析几何AnalyticGeometry第一章矢量与坐标Chapter1VectorsandCoordinates标量scalar矢量vector坐标coordinate空间space系统system代数algebra量quantity计算calculation力学mechanics物理学physics解solution概念concept长度length面积area体积volume唯一displacement大小magnitude方向direction线段linesegment又向线段linesegment始点initialpoint终点terminalpoint模module等于equalto零zero平行四边形parallelogram邻边adjacentside折线brokenline法则rule共线collinear共面coplanar加法运算additiveoperation三角形triangle对角线diagonal平移translation交换律lawofcommutation结合律lawofassociation分配率lawofdistribution乘法multiplication分解decomposition系数coefficient基底base等式equality三棱形triangularprism六面体hexahedron平分线bisector连线connectingline线性相关lineardependence线性无关linearindependence线性组合linearcombination标架frame直角rightangle仿射affine左旋/手标架left-handedframe右旋/手标架right-handedframe空间矢量spacevector笛卡尔坐标系cartesiancoordinatesystem第一象限firstquadrant分母denominator分子molecular仿射坐标系affinecoordinatesystem坐标平面coordinateplane坐标轴coordinateaxis定点vertex重心barycenter中点medianpoint中线medianline射影projection射影矢量projectivevector射线ray垂直perpendicularity夹角includedangle余弦cosine解析几何中的英文单词和短语方向余弦directioncosine正弦sine反交换anti-commutative反矢量inversevector垂足pedal两倍two-fold混合积mixedproduct数性积/内积innerproduct绝对值absolutevalue单位矢量unitvector零矢量zerovector平方square平方和sumofsquares高height高线altitude距离distance分量component左手系left-handedsystem右手系right-handedsystem棱/边edge正数positivenumber复数complexnumber符号symbol初等几何elementarygeometry四面体tetrahedron矢量积crossproduct三重向量基triplevectorproduct实数域realnumberfield克拉默法则Cramerrule拉格朗日恒等式Lagrangeidentity第二章轨迹与方程Chapter2LociandEquations轨迹locus方程equation平面plane实数realnumber对应correspondence曲线curve曲面surface直线straightline充要条件（当且仅当）ifandonlyif图/图标graph圆circle半径radius公式formula原点origin圆心centerofcircle反比proportionbyinversion参数parameter区间interval对称的symmetric定点fixedpoint准方程quasi-equation一次方程linearequation法矢量normalvector重合coincidence交角intersectionangle交点intersectionpoint坐标系coordinatesystem轴axis有向角directedangle旋轮线/摆线cycloid拱形arch尖点cusp切线tangentline切点/触点tangentpoint渐进切线asymptotictangent渐伸线/切展线involvent星形线asteroid初等函数elementaryfunction椭圆ellipse斜率slope等价equivalence抛物线parabola心形线cardioid抛物柱面paraboliccylinder虚曲面imaginarysurface二次方程quadraticequation一元二次方程quadraticequationwithonevariable配方completesquare球/球面sphere圆柱面cylinder椭圆柱面ellipticcylinder双曲柱面hyperboliccylinder母线generators/generatrix准线directrix质点particle角速度angularvelocity维维安尼曲线vivianicurve螺旋线spiral螺旋面spiralsurface射影柱面projectivecylinder右手坐标系right-handedcoordinatesystem圆锥cone圆锥面conesurface因式/因子factor因式分解factoring联立方程simultaneousequations第三章平面与空间直线Chapter3PlanesandStraightLinesinSpace方位azimuth截距式interceptform常数constant垂线verticalline径矢radiusofvector异号oppositesign对边oppositeside方向矢量directionvector离差dispersion相交intersection不等式inequality二面角interfacialangle相关correlate标准方程standardequation方向数directionnumber射影平面projectiveplane公垂线commonperpendicular直线束penciloflines平面束planepencil/pencilofplanes平行平面束pencilofparallelplanes平行平面parallelplanes平行切线paralleltangents平行移动paralleltranslation第四章柱面、锥面、旋转曲面与二次曲面Chapter4Cylinders,ConeSurfaces,RotationSurfacesandQuadraticSurfaces二次曲面quadraticsurface旋转曲面rotationsurface齐次方程homogeneousequation直线族familyofstraightlines二次锥面quadraticcone虚锥面imaginarycone实轴realaxis虚轴imaginaryaxis环面torus椭球面ellipsoid旋转椭球面ellipsoidofrevolution旋转抛物面paraboloidofrevolution单叶univalent旋转轴rotationaxis定直线fixedline主平面principalplane主轴principalaxis对称平面symmetryplane长半轴semi-majoraxis短半轴semi-minoraxis虚半轴imaginarysemi-axis长方体cuboid长轴majoraxis短轴minoraxis端口/线/面section主截线/面principalsection分割/切断segmentation截割cutting曲面图形surfacechart双曲面hyperboloid单叶双曲面hyperboloidofonesheet双曲线hyperbola单叶旋转双曲面hyperboloidofonesheetofrevolution双叶双曲面hyperboloidoftwosheets旋转双叶双曲面hyperboloidoftwosheetsofrevolution双曲抛物面hyperbolicparaboloid马鞍曲面anticlasticsurface无心二次曲面quadraticsurfacewithoutcenter中心center对称中心symmetriccenter对称轴symmetricaxis焦点focus矩形rectangle弧arc直纹曲面ruledsurface第五章二次曲线的一般理论Chapter5GeneralTheoryofQuadraticCurves二次曲线quadraticcurve虚数imaginarynumber虚元素imaginaryelement虚点imaginarypoint共轭虚点conjugateimaginarypoints共轭虚数conjugateimaginarynumber虚矢量imaginaryline虚系数imaginarycoefficient偏导数partialderivative复点complexpoint复矢量complexvector对角元素diagonalelement行列式determinant行row列column弦chord椭圆型elliptictype抛物型parbolictype双曲型hyperbolictype渐进方向asymptoticdirection虚方向imaginarydirction中心直线centralline中心二次曲线quadraticcurvewithcenter无心二次曲线quadraticcurvewithoutcenter中心曲线centralcurve无心曲线noncentralcurve正常点properpoint切线方程tangentialequation恒等式identity奇异点/奇点singularpoint中心轨迹midpointchords主方向principaldirection主直径principaldiameter共轭方向conjugatedirection共轭直径conjugatediameter共轭弦conjugatechord特征方程characteristicequation特征根characteristicvalue坐标变换transformationofcoordinates判别式discriminant旋转轴rotationaxis虚圆imaginaryellipse二次项quadraticelement旋转角angleofrotation可逆变换inversetransformation余切cotangent成比例proportional增广矩阵augmentedmatrix共轭虚直线conjugateimaginaryline不变量invariant多项式polynomial三角函数trigonometricfunction柯西-施瓦茨不等式Cauchy-Schwarzinequality第六章二次曲面的一般理论Chapter6CenraltheoryofQuadraticSurfaces二重根doubleroot主子式principalminordeterminant虚根imaginaryroot实根realroot径面radialplane矩阵matrix切平面tangentplane主径面principalradialplane齐次线性变换homogeneousl