A Treatise on Special Or Elementary Geometry, Bände 1-2Sheldon, 1872 - 1 Seiten |
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Seite xi
... Tangent Planes ... 218-219 Spherical Triangles .. 219-226 Polar or Supplemental Triangles .. 226-228 Quadrature of the Surface of the Sphere .. 229-231 Lunes ...... 231-235 Volume of Sphere .. 235-239 PART III . AN ADVANCED COURSE IN ...
... Tangent Planes ... 218-219 Spherical Triangles .. 219-226 Polar or Supplemental Triangles .. 226-228 Quadrature of the Surface of the Sphere .. 229-231 Lunes ...... 231-235 Volume of Sphere .. 235-239 PART III . AN ADVANCED COURSE IN ...
Seite 20
... Tangent to a circle is a straight line which touches the circumference , but does not intersect it , how far soever the line be produced . 54. A Secant is a straight line which intersects the circumfer- ence in two points . Ex . 1 ...
... Tangent to a circle is a straight line which touches the circumference , but does not intersect it , how far soever the line be produced . 54. A Secant is a straight line which intersects the circumfer- ence in two points . Ex . 1 ...
Seite 82
... tangent to the circumference . DEM . The line touches the circumference because the extremity of the radius is in ... tangent ( 53 ) . Q. E. D. 173. COR . - Conversely , A tangent to a circumference is perpen- dicular to a radius at the ...
... tangent to the circumference . DEM . The line touches the circumference because the extremity of the radius is in ... tangent ( 53 ) . Q. E. D. 173. COR . - Conversely , A tangent to a circumference is perpen- dicular to a radius at the ...
Seite 83
... tangent , the arcs intercepted between the intersections and the point of tangency are equal . DEM . - Let the secant LM be parallel to the tangent RS ; then is CP EP . = For , draw the radius OP to the point of tangency ; it will be ...
... tangent , the arcs intercepted between the intersections and the point of tangency are equal . DEM . - Let the secant LM be parallel to the tangent RS ; then is CP EP . = For , draw the radius OP to the point of tangency ; it will be ...
Seite 84
... to afford models for describing the process . In this case an arc should be drawn first , and all trace of the centre obliterated . Then proceed as directed . 9. Prob . - To draw a tangent to a 84 ELEMENTARY PLANE GEOMETRY .
... to afford models for describing the process . In this case an arc should be drawn first , and all trace of the centre obliterated . Then proceed as directed . 9. Prob . - To draw a tangent to a 84 ELEMENTARY PLANE GEOMETRY .
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A Treatise on Special Or Elementary Geometry: In Four Parts Edward Olney Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
ABCD adjacent altitude angle or arc bisect centre chord circle circumference coincide common point conceive construct cosec cosine cotangent DEM.-Let diagonals diameter diedral distance divided draw drawn equal angles equiangular equilateral equivalent exterior angle facial angles figure frustum geometrical given line given point Hence hypotenuse included angle inscribed intersect isosceles less let fall locus LOGARITHMIC FUNCTIONS lune measured middle point number of sides parallel parallelogram parallelopiped passing pendicular perpendicular plane triangle prism Prob Prob.-To produced project the triangle PROP PROPOSITION pyramid quadrant quadrilateral radii radius rectangle regular polygon revolve right angled triangle secant secant line similar similar triangles sine solution sphere spherical angle spherical triangle square straight line student SUG's surface symmetrical tang tangent Theorem.-The triangle ABC triedral trigonometrical trigonometrical functions values vertex vertices whence
Beliebte Passagen
Seite 219 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Seite 111 - If the diagonals of a parallelogram are equal, the figure is a rectangle.
Seite 130 - 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 will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Seite 33 - Cut out two such triangles and try it Ex. 6. If you have two triangles with only two sides of one respectively equal to two sides of the other, can you make one fit as a pattern on the other ? Try it. Ex. 7. If you have two triangles with two sides in one equal respectively to two sides in the other, and the included angle in one greater than in the other, how is it with the third sides of the triangles ? 76.
Seite 109 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Seite 106 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Seite 250 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Seite 245 - If from any point there extend two lines tangent to a circumference, the angle contained by the tangents is double the angle contained by the line joining the points of contact and the radius extending to one of them.
Seite 141 - Hence, the area of a trapezoid is equal to the product of its altitude by the line connecting the middle points of the sides which are not parallel.
Seite 81 - In the same or in equal circles, of two unequal chords, the less is at the greater distance from the centre. DEM. — Let CE < AB, then is the perpendicular OD, which measures the distance of CE from the centre, greater than OD' •which measures the distance of AB from the centre.