Elements of Geometry, Conic Sections, and Plane TrigonometryHarper & Bros., 1877 - 443 Seiten |
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Seite 5
... Parabola . ......... .. 203 Exercises on the Parabola . 217 The Ellipse .. 219 Exercises on the Ellipse . The Hyperbola ............... . Exercises on the Hyperbola ... 238 240 262 PLANE TRIGONOMETRY . Page Elementary Principles ...
... Parabola . ......... .. 203 Exercises on the Parabola . 217 The Ellipse .. 219 Exercises on the Ellipse . The Hyperbola ............... . Exercises on the Hyperbola ... 238 240 262 PLANE TRIGONOMETRY . Page Elementary Principles ...
Seite 9
... parabola cut off by a chord is two thirds of the circumscribing parallelogram . After Archimedes comes Apollonius of Perga , in Pamphylia , born about 250 B.C. He studied in the Alexandrian school under the successors of Euclid , and so ...
... parabola cut off by a chord is two thirds of the circumscribing parallelogram . After Archimedes comes Apollonius of Perga , in Pamphylia , born about 250 B.C. He studied in the Alexandrian school under the successors of Euclid , and so ...
Seite 10
... parabola is two thirds of that of the circumscribing parallelogram ; and he also showed what was the ratio of elliptic areas to their circumscribing circles , and of solids formed by the revolution of the different sections to their ...
... parabola is two thirds of that of the circumscribing parallelogram ; and he also showed what was the ratio of elliptic areas to their circumscribing circles , and of solids formed by the revolution of the different sections to their ...
Seite 203
... Parabola , The Ellipse , and The Hyperbola . PARABOLA . Definitions . 1. A parabola is a plane curve , every point of which is equally distant from a given fixed point and a given straight line . 2. The fixed point is called the focus ...
... Parabola , The Ellipse , and The Hyperbola . PARABOLA . Definitions . 1. A parabola is a plane curve , every point of which is equally distant from a given fixed point and a given straight line . 2. The fixed point is called the focus ...
Seite 204
... parabola , and the point V , where the axis meets the curve , is called the principal vertex of the parabo- la , or simply the vertex . It is evident , from Def . 1 , that FV = VH ; that is , a perpendic ular drawn from the focus to the ...
... parabola , and the point V , where the axis meets the curve , is called the principal vertex of the parabo- la , or simply the vertex . It is evident , from Def . 1 , that FV = VH ; that is , a perpendic ular drawn from the focus to the ...
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Häufige Begriffe und Wortgruppen
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 line 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
Beliebte Passagen
Seite 68 - Any two rectangles are to each other as the products of their bases by their altitudes.
Seite 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.
Seite 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...
Seite 64 - BEC, taken together, are measured by half the circumference ; hence their sum is equal to two right angles.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 177 - THEOREM. The sum of the sides of a spherical polygon, is less than the circumference of a great circle. Let...
Seite 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.