Elementary Geometry, Plane and Solid: For Use in High Schools and Academies |
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Page 3
... pass through the same two points . That is to say , if two straight lines pass through the same two points , they must occupy the same position , and there is no point of one which does not also lie on the other . This is sometimes ...
... pass through the same two points . That is to say , if two straight lines pass through the same two points , they must occupy the same position , and there is no point of one which does not also lie on the other . This is sometimes ...
Page 13
... passing twice over the same portion of the line . Any figure which can be traced in a similar way , starting at one point and returning to the same point , is called a closed figure . DA If a closed figure is made up wholly of segments ...
... passing twice over the same portion of the line . Any figure which can be traced in a similar way , starting at one point and returning to the same point , is called a closed figure . DA If a closed figure is made up wholly of segments ...
Page 18
... pass through one point and each intersects the other two . How many points of intersection are there ? 9. Choose three points in a plane , not in the same straight line , and join each point to both the others . How many straight lines ...
... pass through one point and each intersects the other two . How many points of intersection are there ? 9. Choose three points in a plane , not in the same straight line , and join each point to both the others . How many straight lines ...
Page 19
... pass through two points . § 4 . ( 2 ) Plane Surface or Plane - a surface such that every straight line joining two points of it lies wholly on the surface . § 7 . ( 3 ) Geometrical Figure - any combination of points , lines , and sur ...
... pass through two points . § 4 . ( 2 ) Plane Surface or Plane - a surface such that every straight line joining two points of it lies wholly on the surface . § 7 . ( 3 ) Geometrical Figure - any combination of points , lines , and sur ...
Page 27
... [ why ? ] ; and the side AB was chosen equal to the given line - segment m . Hence the triangle CAB fulfils the given conditions . EXERCISES 1. Under what conditions would the circle CDE pass 37-39 ] TRIANGLES AND PARALLELOGRAMS 27 27.
... [ why ? ] ; and the side AB was chosen equal to the given line - segment m . Hence the triangle CAB fulfils the given conditions . EXERCISES 1. Under what conditions would the circle CDE pass 37-39 ] TRIANGLES AND PARALLELOGRAMS 27 27.
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Other editions - View all
Elementary Geometry, Plane and Solid; for Use in High Schools and Academies Thomas F 1859-1945 Holgate No preview available - 2018 |
Elementary Geometry Plane and Solid: For Use in High Schools and Academies Thomas F. Holgate No preview available - 2015 |
Common terms and phrases
ABCD adjacent angles altitude angle formed apothem base bisector bisects called centre chord circumscribed coincide common convex convex polygon COROLLARY DEFINITION diagonals diameter dicular dihedral angle draw equal angles equal in area equiangular equidistant EXERCISES face angles figure given circle given line-segment given plane given point given straight line greater Hence hypotenuse identically equal interior angles isosceles triangle lateral area lateral edges lateral surface length magnitudes measure meet mid-point number of sides opposite sides parallel planes parallelepiped parallelogram pass perimeter perpen plane angles point of intersection polyhedral angle polyhedron prism Proof Prop PROPOSITION pyramid quadrilateral radii radius ratio rectangle regular polygon required to prove respectively right triangle segment side BC similar sphere spherical angle spherical polygon spherical triangle square subtended supplementary angle tangent tetrahedron theorem triangle ABC triangle is equal trihedral vertex volume
Popular passages
Page 187 - 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.
Page 207 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.
Page 78 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Page 45 - Prove that, if two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less.
Page 231 - A polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a, pentagon; one of six sides, a hexagon ; one of seven sides, a heptagon ; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon.
Page 95 - 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. Given A ABC and A'B'C...
Page 200 - The area of a triangle is equal to half the product of its base by its altitude.
Page 161 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 201 - Two parallelograms are similar when they have an angle of the one equal to an angle of the other, and the including sides proportional.
Page 29 - 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.