A Treatise on Special Or Elementary Geometry: Including an Elementary, and Also, in Part III, a Higher Course, in Plane, Solid, and Spherical Geometry; and Plane and Spherical Trigonometry, with the Necessary TablesSheldon, 1879 - 440 Seiten |
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Seite 3
... , lines , and solids . These may also be said to constitute the subject - matter of the science . LINES . 14. A Line is the path of a THE GEOMETRICAL CONCEPTS . 3 SECTION THE GEOMETRICAL CONCEPTS Defined and Illustrated 3-11.
... , lines , and solids . These may also be said to constitute the subject - matter of the science . LINES . 14. A Line is the path of a THE GEOMETRICAL CONCEPTS . 3 SECTION THE GEOMETRICAL CONCEPTS Defined and Illustrated 3-11.
Seite 4
... path indicated by the mark to B. The path thus traced is a line . Since a true point has no size , a line has no breadth , though the marks by which we represent lines have some breadth . The first and third lines in the figure are each ...
... path indicated by the mark to B. The path thus traced is a line . Since a true point has no size , a line has no breadth , though the marks by which we represent lines have some breadth . The first and third lines in the figure are each ...
Seite 5
... path of a ball thrown into the air , in any direction except directly up , represents a curved line . Most ⚫ of the lines seen in nature are curved , as the edges of leaves , the shore of a river or lake , etc. Sometimes a path like ...
... path of a ball thrown into the air , in any direction except directly up , represents a curved line . Most ⚫ of the lines seen in nature are curved , as the edges of leaves , the shore of a river or lake , etc. Sometimes a path like ...
Seite 6
... path be like ? Ex . 2. If the figure OMNP , Fig . 9 , be conceived as revolved about OP , what kind of a path will MN trace ? What kind of paths will PN and OM trace ? Ans . One path will be like the surface of a joint of stove - pipe ...
... path be like ? Ex . 2. If the figure OMNP , Fig . 9 , be conceived as revolved about OP , what kind of a path will MN trace ? What kind of paths will PN and OM trace ? Ans . One path will be like the surface of a joint of stove - pipe ...
Seite 8
... path of a surface in motion . ILL - Suppose you have a block of wood like that represented in Fig . 12 , with all its corners ( angles ) square corners ( right angles ) . Hold it still in your fingers a moment , and fix your mind upon ...
... path of a surface in motion . ILL - Suppose you have a block of wood like that represented in Fig . 12 , with all its corners ( angles ) square corners ( right angles ) . Hold it still in your fingers a moment , and fix your mind upon ...
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ABCD adjacent altitude angle or arc bisect centre chord circle circumference coincide common point conceive construct cosec cosine cotangent DEM.-Let diagonals diameter dicular diedral distance divided draw drawn edge equal angles equiangular equilateral equivalent exterior angle facial angles figure frustum Geometry given line given point greater Hence hypotenuse included angle inscribed intersect isosceles less let fall locus logarithms lune measured middle point opposite sides parallel parallelogram parallelopiped passing pendicular perpen perpendicular plane triangle prism Prob Prob.-To project the triangle PROP PROPOSITION pyramid quadrant quadrilateral radii radius rectangle regular polygon revolve right angled triangle secant secant line similar similar triangles sine solid solution sphere spherical angle spherical triangle square straight line student SUG's surface symmetrical tangent Theorem.-The triangle ABC triedral trigonometrical functions vertex vertices whence
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Seite 232 - 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 41 - The homologous sides of similar triangles are to each other as the square roots of their areas. This theorem is involved in the theorem that the areas of similar triangles are to each other as the squares of their homologous sides.
Seite 203 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Seite 131 - Theorem. — The area of a trapezoid is equal to the product of its altitude...
Seite 217 - If two semicircumferences of great circles intersect on the surface of a hemisphere, the sum of the two opposite triangles thus formed is equivalent to a lune whose angle is that included by the semicircumferences. DEM. — Let the semicircumferences CEB and DEA intersect at E on the surface of the...
Seite 34 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Seite 128 - Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other.
Seite 276 - Find the locus of a point the sum of whose distances from two fixed intersecting lines is constant, ie, is equal to a given line.
Seite 96 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Seite 206 - 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.