The Elements of Plane and Solid Geometry: With Numerous ExercisesD.C. Heath & Company, 1890 - 393 Seiten |
Im Buch
Ergebnisse 1-5 von 44
Seite vii
... Tangent Planes .. Spherical Triangles and Polygons ..... Relation of a Spherical Polygon to a Polyedral Angle . Symmetrical Spherical Triangles .... Polar Triangles ... Relative Areas of Spherical Figures . Exercises . Theorems ...
... Tangent Planes .. Spherical Triangles and Polygons ..... Relation of a Spherical Polygon to a Polyedral Angle . Symmetrical Spherical Triangles .... Polar Triangles ... Relative Areas of Spherical Figures . Exercises . Theorems ...
Seite 75
... tangent to a circle is any straight line which meets the circumference , but , being pro- A- duced , does not cut it ... tangent to the circle at the point P. 183. Two circles are tangent to each other when they are tangent to the same ...
... tangent to a circle is any straight line which meets the circumference , but , being pro- A- duced , does not cut it ... tangent to the circle at the point P. 183. Two circles are tangent to each other when they are tangent to the same ...
Seite 77
... tangent to the circumference , as ABCD . The circle is then said to be inscribed in the polygon . B A 192. From the definition of a circle it follows : ( 1 ) The distance of a point from the centre of a circle is less than , equal to ...
... tangent to the circumference , as ABCD . The circle is then said to be inscribed in the polygon . B A 192. From the definition of a circle it follows : ( 1 ) The distance of a point from the centre of a circle is less than , equal to ...
Seite 85
... tangent to the O at A. Q. E.D. 210. COR . 1. Conversely , a tangent to a circle at any point is perpendicular to the radius drawn to that point . 211. COR . 2. The perpendicular to a tangent at the point of tangency passes though the ...
... tangent to the O at A. Q. E.D. 210. COR . 1. Conversely , a tangent to a circle at any point is perpendicular to the radius drawn to that point . 211. COR . 2. The perpendicular to a tangent at the point of tangency passes though the ...
Seite 86
... tangent and CD is a secant . To prove arc CE = arc DE . Proof . Draw the radius OE to the pt . of contact E. Then OE is to AB , and to it || CD . ... arc CE = arc DE . ( 210 ) ( 71 ) ( 201 ) CASE III . When AB , CD are tangents . To ...
... tangent and CD is a secant . To prove arc CE = arc DE . Proof . Draw the radius OE to the pt . of contact E. Then OE is to AB , and to it || CD . ... arc CE = arc DE . ( 210 ) ( 71 ) ( 201 ) CASE III . When AB , CD are tangents . To ...
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Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
ABCD adjacent angles altitude angles are equal base bisect bisector called centre chord circumference circumscribed coincide common cone of revolution Cons construct cylinder diagonals diameter diedral angle distance divided draw equally distant equivalent EXERCISES exterior angle faces feet Find the area Find the volume frustum given circle given line given point given straight line homologous homologous sides hypotenuse inches intersection isosceles triangle lateral area lateral edges Let ABC meet middle point number of sides parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced Proposition Proposition 13 pyramid quadrilateral radii radius ratio rectangle rectangular parallelopiped regular inscribed regular polygon right angles segment similar slant height sphere spherical polygon spherical triangle square surface symmetrical tangent tetraedron Theorem triangle ABC triangular prism triedral vertex
Beliebte Passagen
Seite 74 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Seite 188 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Seite 45 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.
Seite 137 - Terms of the proportion. The first and fourth terms are called the Extremes, and the second and third the Means.
Seite 12 - AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums will be equal.
Seite 206 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Seite 97 - BAC, inscribed in a segment greater than a semicircle, is an acute angle ; for it is measured by half of the arc BOC, less than a semicircumference.
Seite 334 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Seite 12 - LET it be granted that a straight line may be drawn from any one point to any other point.
Seite 253 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.