Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
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... PROPORTIONAL LINES SIMILAR POLYGONS TRANSVERSALS LINES ON THE CIRCLE PROBLEMS CERR 63 67 79 83 90 93 97 BOOK IV . REGULAR POLYGONS , AND THE CIRCLE 105 MEASUREMENT OF THE CIRCLE . 112 SOLID GEOMETRY . BOOK V. STRAIGHT LINES , AND PLANES ...
... PROPORTIONAL LINES SIMILAR POLYGONS TRANSVERSALS LINES ON THE CIRCLE PROBLEMS CERR 63 67 79 83 90 93 97 BOOK IV . REGULAR POLYGONS , AND THE CIRCLE 105 MEASUREMENT OF THE CIRCLE . 112 SOLID GEOMETRY . BOOK V. STRAIGHT LINES , AND PLANES ...
Página 63
... proportional , when A : B = B : C. B is called a mean proportional between A and C. A C 3. Since the form A : BC : D is equivalent to B D ' the following transformations may be made by simple alge- braic operations . Multiplying both ...
... proportional , when A : B = B : C. B is called a mean proportional between A and C. A C 3. Since the form A : BC : D is equivalent to B D ' the following transformations may be made by simple alge- braic operations . Multiplying both ...
Página 64
... proportional between 6 and 24 ; between 5 and 10 . SCHOLIUM . It is important for the student to remember , that ... proportional , the first is to the third as the second is to the fourth ; that is , they are proportional by alternation ...
... proportional between 6 and 24 ; between 5 and 10 . SCHOLIUM . It is important for the student to remember , that ... proportional , the first is to the third as the second is to the fourth ; that is , they are proportional by alternation ...
Página 65
... proportional , their like powers or roots are also proportional . 7. Since A MA B mB " it follows that A : B = mA : m B , where m may be a whole number or fraction ; that is , equimultiples , or like parts , of two quantities , have the ...
... proportional , their like powers or roots are also proportional . 7. Since A MA B mB " it follows that A : B = mA : m B , where m may be a whole number or fraction ; that is , equimultiples , or like parts , of two quantities , have the ...
Página 66
... proportional . A 13. If or , A BC : D , B B and or , B : F = G : H ; F H A CXG then or A : FCXG : DXH . F DXH ' EXERCISE 3. If A : C = B : D , and A : E = B : F , prove that CED : F. EXERCISE 4. If A : CB : D , and E : C = F : D , prove ...
... proportional . A 13. If or , A BC : D , B B and or , B : F = G : H ; F H A CXG then or A : FCXG : DXH . F DXH ' EXERCISE 3. If A : C = B : D , and A : E = B : F , prove that CED : F. EXERCISE 4. If A : CB : D , and E : C = F : D , prove ...
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.