Elements of Geometry, Conic Sections, and Plane TrigonometryHarper & Bros., 1877 - 443 σελίδες |
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Σελίδα 203
... focus of the parabola , and the given straight line is called the directrix . Ᏼ . D Thus , if a straight line BC , and a point with- out it , F , be given in position in a plane , and the point A be supposed to move in such a manner ...
... focus of the parabola , and the given straight line is called the directrix . Ᏼ . D Thus , if a straight line BC , and a point with- out it , F , be given in position in a plane , and the point A be supposed to move in such a manner ...
Σελίδα 204
... focus , and the vertex of the axis is called the principal vertex . Thus , through the focus F draw GH perpendicular to the di- rectrix ; GV is the axis of the parabola , and the point V , where the axis meets the curve , is called the ...
... focus , and the vertex of the axis is called the principal vertex . Thus , through the focus F draw GH perpendicular to the di- rectrix ; GV is the axis of the parabola , and the point V , where the axis meets the curve , is called the ...
Σελίδα 205
... focus and directrix of a parabola being given , to describe the curve . FIRST METHOD . By points .. Let F be the focus , and Bb the directrix of a parabola . Through F draw DC perpendic- ular to Bb , and bisect FD in V ; then , since DV ...
... focus and directrix of a parabola being given , to describe the curve . FIRST METHOD . By points .. Let F be the focus , and Bb the directrix of a parabola . Through F draw DC perpendic- ular to Bb , and bisect FD in V ; then , since DV ...
Σελίδα 206
... focus F. Then slide the side of the square DE along the ruler BC , and at the same time keep the thread continually stretched by means of the point of a pencil A in contact with the square ; the pencil will describe one part of the ...
... focus F. Then slide the side of the square DE along the ruler BC , and at the same time keep the thread continually stretched by means of the point of a pencil A in contact with the square ; the pencil will describe one part of the ...
Σελίδα 207
... focus is greater or less than its distance from the directrix . PROPOSITION III . THEOREM . The straight line which bisects the angle contained by two lines drawn from the same point in the curve , the one to the focus and the other ...
... focus is greater or less than its distance from the directrix . PROPOSITION III . THEOREM . The straight line which bisects the angle contained by two lines drawn from the same point in the curve , the one to the focus and the other ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle ACB angle BAC base bisect centre centre of symmetry chord circle circumference cone conjugate conjugate hyperbola Cosine Cotang curve described diagonals diameter directrix distance divided draw ellipse equal to AC equilateral equivalent figure foci frustum given angle given point given straight line greater half Hence hyperbola hypothenuse inscribed intersection join latus rectum less Let ABC line drawn logarithm major axis meet multiplied number of sides ordinate parabola parallel to BC parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced projection Prop PROPOSITION pyramid quadrant quadrilateral radical axis radii radius ratio rectangle regular polygon right-angled triangle Scholium secant segment side AC similar sine solid angle sphere spherical square subtangent symmetrical Tang tangent THEOREM transverse axis triangle ABC vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 68 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 35 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 187 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Σελίδα 64 - BEC, taken together, are measured by half the circumference ; hence their sum is equal to two right angles.
Σελίδα 71 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Σελίδα 23 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Σελίδα 20 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 124 - The area of a circle is equal to the product of its circumference by half the radius.* Let ACDE be a circle whose centre is O and radius OA : then will area OA— ^OAxcirc.
Σελίδα 177 - THEOREM. The sum of the sides of a spherical polygon, is less than the circumference of a great circle. Let...
Σελίδα 27 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.