Elements of GeometryH. Holt, 1881 - 399 sider |
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Side vii
... Circumscribed Figures .. 103 III . Properties of Two Circles .... 112 IV . Problems relating to the Circle . Theorems for Exercise ..... 117 126 BOOK IV . OF AREAS . I. Areas of Rectangles ... 132 II . Areas of Plane Figures . 138 III ...
... Circumscribed Figures .. 103 III . Properties of Two Circles .... 112 IV . Problems relating to the Circle . Theorems for Exercise ..... 117 126 BOOK IV . OF AREAS . I. Areas of Rectangles ... 132 II . Areas of Plane Figures . 138 III ...
Side viii
... Circumscribed Regular Polygons .. 214 II . Construction of Regular Polygons ..... 219 III . Areas and Perimeters of Regular Polygons and of the Circle .. 224 Exercises .. 235 IV . Maximum and Minimum Figures . 237 Theorems for Exercise ...
... Circumscribed Regular Polygons .. 214 II . Construction of Regular Polygons ..... 219 III . Areas and Perimeters of Regular Polygons and of the Circle .. 224 Exercises .. 235 IV . Maximum and Minimum Figures . 237 Theorems for Exercise ...
Side 102
... triangles are identically equal ; namely , the side PM is equal to its corresponding side PN , and the angle OPM to OPN . Q.E.D. CHAPTER II . INSCRIBED AND CIRCUMSCRIBED FIGURES Definitions . 228. 102 BOOK III . THE CIRCLE .
... triangles are identically equal ; namely , the side PM is equal to its corresponding side PN , and the angle OPM to OPN . Q.E.D. CHAPTER II . INSCRIBED AND CIRCUMSCRIBED FIGURES Definitions . 228. 102 BOOK III . THE CIRCLE .
Side 103
... circumscribed about the figure . 229. Def . A figure is said to be circumscribed about a circle when all its sides are tangents to the circle . The circle is then said to be in- scribed in the figure . 230. Def . An inscribed angle is ...
... circumscribed about the figure . 229. Def . A figure is said to be circumscribed about a circle when all its sides are tangents to the circle . The circle is then said to be in- scribed in the figure . 230. Def . An inscribed angle is ...
Side 105
... , and remarking that Angle CTB angle DTBangle CTD , - Arc CDB'T arc DB'T arc CD , = we haye angle CTD = angle of arc CD which does not in- clude T. Q.E.D. Corollary 1. The angle of the arc CD is , INSCRIBED AND CIRCUMSCRIBED FIGURES . 105.
... , and remarking that Angle CTB angle DTBangle CTD , - Arc CDB'T arc DB'T arc CD , = we haye angle CTD = angle of arc CD which does not in- clude T. Q.E.D. Corollary 1. The angle of the arc CD is , INSCRIBED AND CIRCUMSCRIBED FIGURES . 105.
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Vanlige uttrykk og setninger
ABCD adjacent angles altitude angle AOB angle arc base bisect centre chord circle circumscribed coincide Conclusion cone conical surface construction corresponding curve diagonals diameter dicular dihedral angle distance divided draw edge angle ellipse equal angles equally distant exterior angle face angles figure foci frustrum geometry given greater Hence hyperbola Hypothesis identically equal indefinitely inscribed isosceles Join length line of intersection locus magnitude meet middle point number of sides opposite angles opposite sides parabola parallel planes parallelogram parallelopiped pass perpen plane MN point of intersection polyhedral angle polyhedron prism Proof pyramid Q.E.D. Corollary Q.E.D. THEOREM quadrilateral radii radius ratio rect rectangle reflex angle regular polygon right angles Scholium segments slant height solid sphere spherical triangle square straight angle straight line surface tangent trapezoid triangles are identically vertex vertices
Populære avsnitt
Side 146 - In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the sum of the squares on the other two sides by twice the rectangle contained by either side and the projection on it of the other side.
Side 184 - 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.
Side 44 - Every point in the bisector of an angle is equally distant from the sides of the angle...
Side 149 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 45 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Side 103 - A rectilineal figure is said to be described about a circle, when each side of the circumscribed figure touches the circumference of the circle. V. In like manner, a circle is said to be inscribed...
Side 235 - ten decimals are sufficient to give the circumference of the earth to the fraction of an inch, and thirty decimals would give the circumference of the whole visible universe to a quantity imperceptible with the most powerful microscope.
Side 90 - The sum of the three straight lines drawn from any point within a triangle to the three vertices, is less than the sum and greater than the half sum of the three sides of the triangle (I . 33, 66).
Side 168 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Side 196 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means.