Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
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... follow . They are so interwoven into higher mathematics , that it has become necessary for the student's progress to introduce them into our text- books of elementary geometry . Book IX . is a brief introduction to modern geometry . The ...
... follow . They are so interwoven into higher mathematics , that it has become necessary for the student's progress to introduce them into our text- books of elementary geometry . Book IX . is a brief introduction to modern geometry . The ...
Página 24
... follows that AD = DB ( 30,3 ) . The same may be proved of every point in DC . HYPOTH . 2. The point E is out of the perpendicular . TO BE PROVED . EA > EB . PROOF . For every position of the point E , it is evident that one of the lines ...
... follows that AD = DB ( 30,3 ) . The same may be proved of every point in DC . HYPOTH . 2. The point E is out of the perpendicular . TO BE PROVED . EA > EB . PROOF . For every position of the point E , it is evident that one of the lines ...
Página 27
... are supplements of each other . COR . 5. From Cor . 4 it follows , that , if two angles have their sides perpendicular each to each , they will be equal or supplements of each other . A For if A'BL AB , and A'C AC , Book I. ] 27 POLYGONS .
... are supplements of each other . COR . 5. From Cor . 4 it follows , that , if two angles have their sides perpendicular each to each , they will be equal or supplements of each other . A For if A'BL AB , and A'C AC , Book I. ] 27 POLYGONS .
Página 29
... follows ( 14 , 6 ) that AB = CD , AD = BC , A = C , and 4x + p = o + y : hence the opposite sides and angles of a parallelogram are ecial . and EBA = EDU V COR . 2. Two parallels , AD hence △ AEB ≈ CED ( nd BC , included between two ...
... follows ( 14 , 6 ) that AB = CD , AD = BC , A = C , and 4x + p = o + y : hence the opposite sides and angles of a parallelogram are ecial . and EBA = EDU V COR . 2. Two parallels , AD hence △ AEB ≈ CED ( nd BC , included between two ...
Página 32
... follows , that if AD = DB , and AE = EC , then DE || BC ; that is , the line joining the middle points of two sides of a triangle is parallel to the third side . COR . 2. Since DE BF FC , DE = = BC 2 B D C that is , the line joining the ...
... follows , that if AD = DB , and AE = EC , then DE || BC ; that is , the line joining the middle points of two sides of a triangle is parallel to the third side . COR . 2. Since DE BF FC , DE = = BC 2 B D C that is , the line joining the ...
Términos y frases comunes
AB² ABCD AC² adjacent angles altitude angles are equal anharmonic ratio bisect called centre chord circle circumference circumscribed polygon cone congruent construct cylinder diagonals diameter dihedrals distance divided draw equal altitudes equal bases equally distant equations equiangular EXERCISE exterior angle face angles formed frustum Geometry harmonically hence homologous HYPOTH infinite number inscribed angle intersection lateral edges line joining lines drawn locus middle point number of sides Olney's opposite sides P₁ parallel lines parallelogram parallelopiped pass perpendicular plane angle point of contact polar pole polyhedral polyhedron prism Problem PROOF proportional PROVED pyramid quadrilateral radical axis radii radius rectangle regular polygon right angles SCHOLIUM segments solid angle sphere spherical excess spherical polygon spherical triangle square straight line symmetrical tangent Theorem triangle ABC trihedrals vertex vertices
Pasajes populares
Página 19 - IF two triangles have two sides of the one equal to two sides of the...
Página 34 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Página 14 - 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, &c.
Página 75 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Página 170 - Two prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes; prisms having equal altitudes are to each other as their bases ; prisms having equivalent bases and equal altitudes are equivalent.
Página 69 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.