The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 38.
Σελίδα 139
... curves and curve surfaces by means of their genesis . We are not , however , imperatively tied down to this arrangement ; but whatever method we employ , the description must be adequate , complete , and devoid of superfluous con ...
... curves and curve surfaces by means of their genesis . We are not , however , imperatively tied down to this arrangement ; but whatever method we employ , the description must be adequate , complete , and devoid of superfluous con ...
Σελίδα 208
... curve A'EB ' is also a semicircle . * This secondary series of circles are called sub - contrary or antiparallel to the former : the former name is most frequently used , the latter the more convenient . CHAPTER VIII . GEOMETRY OF THE ...
... curve A'EB ' is also a semicircle . * This secondary series of circles are called sub - contrary or antiparallel to the former : the former name is most frequently used , the latter the more convenient . CHAPTER VIII . GEOMETRY OF THE ...
Σελίδα 221
... curves , and the equations of their tangents , normals , and diameters . In establishing that method , however , a ... curve . When the directing plane cuts one sheet only of the complete cone , the figure is called the ellipse . † 4 ...
... curves , and the equations of their tangents , normals , and diameters . In establishing that method , however , a ... curve . When the directing plane cuts one sheet only of the complete cone , the figure is called the ellipse . † 4 ...
Σελίδα 222
... curve is called the principal diameter or axis of the parabola . 6. The middle of the transverse diameter of the ellipse or hyperbola is called the centre of the curve , and a line drawn through the centre at right angles to that ...
... curve is called the principal diameter or axis of the parabola . 6. The middle of the transverse diameter of the ellipse or hyperbola is called the centre of the curve , and a line drawn through the centre at right angles to that ...
Σελίδα 223
... curve , the property is consequently established . COR . 1. Let B and P be any two points in the parabola PAP ' , and BF , PM their semi - ordinates ; then by the proposition , AF : AM :: BF2 : PM2 , or AF : BF : AM : PM * . Hence , if ...
... curve , the property is consequently established . COR . 1. Let B and P be any two points in the parabola PAP ' , and BF , PM their semi - ordinates ; then by the proposition , AF : AM :: BF2 : PM2 , or AF : BF : AM : PM * . Hence , if ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD angle ABC angle BAC axis bisected centre circle ABC circumference coincide cone conic section construction coordinate planes curve described Descriptive Geometry dicular dihedral angles directrix distance draw edges ellipse equal angles equiangular equimultiples given line given point given straight line greater hence inclination intersection join less Let ABC Let the plane line BC lines drawn magnitudes meet multiple opposite orthograph parabola parallel planes parallelogram parallelopiped perpen perpendicular plane MN plane of projection plane parallel plane PQ prisms profile angles profile plane projecting plane projector Prop Q. E. D. PROPOSITION ratio rectangle rectangle contained rectilineal figure remaining angle respectively right angles SCHOLIUM segment sides six right sphere spherical spherical angle tangent THEOR trace triangle ABC trihedral vertex vertical plane Whence Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 19 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Σελίδα 35 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Σελίδα 4 - AB; but things which are equal to the same are equal to one another...
Σελίδα 128 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Σελίδα 8 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 36 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced...
Σελίδα 21 - BCD, and the other angles to the other angles, (4. 1.) each to each, to which the equal sides are opposite : therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal to one another, AC is parallel (27. 1 .) to DB ; and it was shown to be equal to it. Therefore straight lines, &c.
Σελίδα 65 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Σελίδα 116 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.