Elements of Geometry, Conic Sections, and Plane TrigonometryHarper & Bros., 1877 - 443 σελίδες |
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Σελίδα 110
... perimeters of two regular polygons of the same number of sides are to each other as their homologous sides , and their areas are as the squares of those sides ( B. IV . , Pr . 27 ) . Scholium . The magnitude of the angles of a regular ...
... perimeters of two regular polygons of the same number of sides are to each other as their homologous sides , and their areas are as the squares of those sides ( B. IV . , Pr . 27 ) . Scholium . The magnitude of the angles of a regular ...
Σελίδα 116
... perimeter of the polygon , multiplied by half of GH , or half the radius of the inscribed circle . Therefore the area of a regular polygon , etc. PROPOSITION VIII , THEOREM . The perimeters of two regular 116 GEOMETRY .
... perimeter of the polygon , multiplied by half of GH , or half the radius of the inscribed circle . Therefore the area of a regular polygon , etc. PROPOSITION VIII , THEOREM . The perimeters of two regular 116 GEOMETRY .
Σελίδα 117
... perimeters of the two polygons are to each other as the sides BC , bc ( Pr . I. , Cor . ) ; they are therefore to each other as the radii BG , bg of the circum- scribed circles ; and also as the radii GH , gh of the inscribed circles ...
... perimeters of the two polygons are to each other as the sides BC , bc ( Pr . I. , Cor . ) ; they are therefore to each other as the radii BG , bg of the circum- scribed circles ; and also as the radii GH , gh of the inscribed circles ...
Σελίδα 122
... perimeter multiplied by half of CD ( Pr . 7 ) . Conceive the number of sides of the polygon to be indefinitely increased by continually bisecting the arcs subtended by the sides , its perimeter will approach more nearly to the circumfer ...
... perimeter multiplied by half of CD ( Pr . 7 ) . Conceive the number of sides of the polygon to be indefinitely increased by continually bisecting the arcs subtended by the sides , its perimeter will approach more nearly to the circumfer ...
Σελίδα 123
... perimeters will be to each other as the ra dii of the circumscribed circles ( Pr . 8 ) . Conceive the arcs sub- tended by the sides of the polygons to be continually bisected until the number of sides of the polygons becomes ...
... perimeters will be to each other as the ra dii of the circumscribed circles ( Pr . 8 ) . Conceive the arcs sub- tended by the sides of the polygons to be continually bisected until the number of sides of the polygons becomes ...
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.