The Elements of Plane and Solid Geometry: With Numerous ExercisesD.C. Heath & Company, 1890 - 393 Seiten |
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Seite 74
... diameter . From the definition of a circle , it is evident that all its radii are equal ; and also that all its diameters are equal , and each double the radius . C E A 180. An arc of a circle is any part of the circumfer- ence , as AED ...
... diameter . From the definition of a circle , it is evident that all its radii are equal ; and also that all its diameters are equal , and each double the radius . C E A 180. An arc of a circle is any part of the circumfer- ence , as AED ...
Seite 76
... diameter and a semi - circumference , as DFE . 185. A straight line is inscribed in a circle when its extremities are on the cir- cumference , as AC . A D B 186. An inscribed angle is one whose vertex is in the circumference , and whose ...
... diameter and a semi - circumference , as DFE . 185. A straight line is inscribed in a circle when its extremities are on the cir- cumference , as AC . A D B 186. An inscribed angle is one whose vertex is in the circumference , and whose ...
Seite 78
... diameter divides the circle and the circum- ference into two equal parts , and is greater than any other chord . Ө B Hyp . Let AB be the diameter of the O ACB , and AC any chord not passing through the centre . To prove that AB bisects ...
... diameter divides the circle and the circum- ference into two equal parts , and is greater than any other chord . Ө B Hyp . Let AB be the diameter of the O ACB , and AC any chord not passing through the centre . To prove that AB bisects ...
Seite 82
... which the arc subtends . 205. COR . 4. The locus of the middle point of parallel chords in a circle is the diameter perpendicular to these chords . Proposition 6. Theorem . 206. In the same circle , 82 PLANE GEOMETRY .
... which the arc subtends . 205. COR . 4. The locus of the middle point of parallel chords in a circle is the diameter perpendicular to these chords . Proposition 6. Theorem . 206. In the same circle , 82 PLANE GEOMETRY .
Seite 86
... are equal , the secants are parallel . 216. COR . 2. The straight line joining the points of con- tact of two parallel tangents is a diameter . Proposition 10. Theorem . 217. Through three given points not 86 PLANE GEOMETRY .
... are equal , the secants are parallel . 216. COR . 2. The straight line joining the points of con- tact of two parallel tangents is a diameter . Proposition 10. Theorem . 217. Through three given points not 86 PLANE GEOMETRY .
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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.