Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 σελίδες |
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Σελίδα
... ANHARMONIC RATIO ANHARMONIC PROPERTIES OF THE CIRCLE . Pascal's Theorem Brianchon's Theorem HARMONIC PROPORTION · POLES AND POLARS WITH RESPECT TO A CIRCLE RECIPROCAL POLARS Salmon's Theorem RADICAL AXIS OF CIRCLES . CENTRES OF ...
... ANHARMONIC RATIO ANHARMONIC PROPERTIES OF THE CIRCLE . Pascal's Theorem Brianchon's Theorem HARMONIC PROPORTION · POLES AND POLARS WITH RESPECT TO A CIRCLE RECIPROCAL POLARS Salmon's Theorem RADICAL AXIS OF CIRCLES . CENTRES OF ...
Σελίδα 186
... ) 6 + 2 A + 7A3 . COR . If the segment has but one base , as vol . ABED , the radius r - - O , and we have , vol . ABED = 17r2A + 1πA3 . MODERN GEOMETRY . BOOK IX . * ANHARMONIC RATIO . 186 [ Воок VIII . ELEMENTS OF GEOMETRY .
... ) 6 + 2 A + 7A3 . COR . If the segment has but one base , as vol . ABED , the radius r - - O , and we have , vol . ABED = 17r2A + 1πA3 . MODERN GEOMETRY . BOOK IX . * ANHARMONIC RATIO . 186 [ Воок VIII . ELEMENTS OF GEOMETRY .
Σελίδα 187
... ANHARMONIC RATIO . I. IF A , B , C , and D are four points in a straight line , the ratio AC AD CB DB is called the anharmonic ratio of the four points . This ratio is also expressed by [ ABCD ] , which gives the A order in which the ratio ...
... ANHARMONIC RATIO . I. IF A , B , C , and D are four points in a straight line , the ratio AC AD CB DB is called the anharmonic ratio of the four points . This ratio is also expressed by [ ABCD ] , which gives the A order in which the ratio ...
Σελίδα 188
... ratio . The four letters may be written in twenty- four different orders ; and hence , from four points in a line , six different anharmonic ratios may be formed . ( Write the six anharmonic ratios , and show that three are the ...
... ratio . The four letters may be written in twenty- four different orders ; and hence , from four points in a line , six different anharmonic ratios may be formed . ( Write the six anharmonic ratios , and show that three are the ...
Σελίδα 189
... anharmonic R and PXQXR - 1 , 1 1 1 P X Х 1 . Ꭱ V. DEF . 1. A system of lines passing through a common point is called a pencil . Each line is called a ray ; and the common point , the vertex . Theorem . If a pencil of ... ANHARMONIC RATIO .
... anharmonic R and PXQXR - 1 , 1 1 1 P X Х 1 . Ꭱ V. DEF . 1. A system of lines passing through a common point is called a pencil . Each line is called a ray ; and the common point , the vertex . Theorem . If a pencil of ... ANHARMONIC RATIO .
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 19 - IF two triangles have two sides of the one equal to two sides of the...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.