Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
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... proved . These are therefore given in a distinct form . Exercises and numerical examples are inserted in numbers sufficiently great to fix the truth of the proposition in the mind of the student , without materially increasing the ...
... proved . These are therefore given in a distinct form . Exercises and numerical examples are inserted in numbers sufficiently great to fix the truth of the proposition in the mind of the student , without materially increasing the ...
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... PROVED . 1 . 6 = 4 2 = 8 , 1 \ 2 .. A B 5 6 7 8 с 3 4 F D PROOF . AS AB and CD have the same direction ( 8 ) , their difference of direction with a third line , EF , will be the same ; that is , 28 , 6 = 4 • • · ≤ 28 ( Case 1 ) , TO BE ...
... PROVED . 1 . 6 = 4 2 = 8 , 1 \ 2 .. A B 5 6 7 8 с 3 4 F D PROOF . AS AB and CD have the same direction ( 8 ) , their difference of direction with a third line , EF , will be the same ; that is , 28 , 6 = 4 • • · ≤ 28 ( Case 1 ) , TO BE ...
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... PROVED . 2. 58 , 67 , 23 , 1 = 4 . PROOF . hence 2 = 5 ( 7 ) : * 258 ( Ax . 1 ) . In a similar manner , we may prove the other pairs of alternate angles equal . TO BE PROVED . 3. 26 + 8 = 2R . . PROOF . 28 ( Case 1 ) , < 6 + 2 = 2R ( 4 ) ...
... PROVED . 2. 58 , 67 , 23 , 1 = 4 . PROOF . hence 2 = 5 ( 7 ) : * 258 ( Ax . 1 ) . In a similar manner , we may prove the other pairs of alternate angles equal . TO BE PROVED . 3. 26 + 8 = 2R . . PROOF . 28 ( Case 1 ) , < 6 + 2 = 2R ( 4 ) ...
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And the First Principles of Modern Geometry William Henry Harrison Phillips. TO BE PROVED . PROOF . hence and AB || CD . 58 ( Hypoth . ) , 25 = 2 ( 7 ) : 28 ( Ax . 1 ) , AB | CD ( Case 1 ) . HYPOTH . 3 . 26 + 8 = 2R . TO BE PROVED . AB ...
And the First Principles of Modern Geometry William Henry Harrison Phillips. TO BE PROVED . PROOF . hence and AB || CD . 58 ( Hypoth . ) , 25 = 2 ( 7 ) : 28 ( Ax . 1 ) , AB | CD ( Case 1 ) . HYPOTH . 3 . 26 + 8 = 2R . TO BE PROVED . AB ...
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... Prove this by an auxiliary line , BC . EXERCISE 2. The lines bisecting two adjacent angles are perpendicular to each other . HYPOTH . EC and FC bisect the adja- cent angles BCD and ACD . TO BE PROVED . ECF — R. - A F D E B EXERCISE 3 ...
... Prove this by an auxiliary line , BC . EXERCISE 2. The lines bisecting two adjacent angles are perpendicular to each other . HYPOTH . EC and FC bisect the adja- cent angles BCD and ACD . TO BE PROVED . ECF — R. - A F D E B EXERCISE 3 ...
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.