Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 σελίδες |
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Σελίδα
... POLES AND POLARS WITH RESPECT TO A CIRCLE RECIPROCAL POLARS Salmon's Theorem RADICAL AXIS OF CIRCLES . CENTRES OF SIMILITUDE 165 172 177 183 187 192 194 195 196 198 202 204 205 207 ELEMENTS OF GEOMETRY . GENERAL PRINCIPLES . DEFINITIONS ...
... POLES AND POLARS WITH RESPECT TO A CIRCLE RECIPROCAL POLARS Salmon's Theorem RADICAL AXIS OF CIRCLES . CENTRES OF SIMILITUDE 165 172 177 183 187 192 194 195 196 198 202 204 205 207 ELEMENTS OF GEOMETRY . GENERAL PRINCIPLES . DEFINITIONS ...
Σελίδα 152
... poles , and the diameter the axis , of that circle . COR . 6. All the parallel circles on a sphere have the same axis and poles . • COR . 7. Every great circle divides a sphere and its surface into two congruent parts ; for if the two ...
... poles , and the diameter the axis , of that circle . COR . 6. All the parallel circles on a sphere have the same axis and poles . • COR . 7. Every great circle divides a sphere and its surface into two congruent parts ; for if the two ...
Σελίδα 153
... poles . HYPOTH . CDEF is a circle on a sphere , AB its axis , and A a pole . TO BE PROVED . AC AD = AE = & c . " A PROOF . Since the axis , AB , passes through the centre of the circle , CDEF , at right angles , the triangles AOC , AOD ...
... poles . HYPOTH . CDEF is a circle on a sphere , AB its axis , and A a pole . TO BE PROVED . AC AD = AE = & c . " A PROOF . Since the axis , AB , passes through the centre of the circle , CDEF , at right angles , the triangles AOC , AOD ...
Σελίδα 155
... pole is A , the angle COE and the arc CE have the same measure as the dihedral CAOE : hence CAE = GAH = CAOE = COE = arc CE ; that is , the angle of two arcs of great circles has the same measure as the dihedral of their planes , or as ...
... pole is A , the angle COE and the arc CE have the same measure as the dihedral CAOE : hence CAE = GAH = CAOE = COE = arc CE ; that is , the angle of two arcs of great circles has the same measure as the dihedral of their planes , or as ...
Σελίδα 156
... pole of a great circle , CED , and AC is an arc of a great circle , then ACE R ; for diameter AOB plane CED ( V. , 1 , Def . 2 ) : hence plane ACO CED ( V. , 14 ) , conversely , if CAL CD , each arc passes through the pole of the other ...
... pole of a great circle , CED , and AC is an arc of a great circle , then ACE R ; for diameter AOB plane CED ( V. , 1 , Def . 2 ) : hence plane ACO CED ( V. , 14 ) , conversely , if CAL CD , each arc passes through the pole of the other ...
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.