Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
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Página 34
... diameter is a line passing through the centre , and terminated each way by the circumference ; as , AB . COR . 1. A radius is one - half a diameter : all radii of the same circle are equal ; and they measure the distance of the centre ...
... diameter is a line passing through the centre , and terminated each way by the circumference ; as , AB . COR . 1. A radius is one - half a diameter : all radii of the same circle are equal ; and they measure the distance of the centre ...
Página 35
... diameter divides the circle and its circum- ference into two congruent parts . HYPOTH . AB is a diameter of the circumference ACBD . TO BE PROVED . ACB ADB . PROOF . If the part ACB be turned about the diameter AB , the arc ACB will ...
... diameter divides the circle and its circum- ference into two congruent parts . HYPOTH . AB is a diameter of the circumference ACBD . TO BE PROVED . ACB ADB . PROOF . If the part ACB be turned about the diameter AB , the arc ACB will ...
Página 37
... diameter is the greatest chord . A F E EXERCISE 1. State and prove the converse of this propo- sition . EXERCISE 2. The shortest chord that can be drawn through a given point within a circle is a chord perpendicular to the radius ...
... diameter is the greatest chord . A F E EXERCISE 1. State and prove the converse of this propo- sition . EXERCISE 2. The shortest chord that can be drawn through a given point within a circle is a chord perpendicular to the radius ...
Página 38
... ( part 2 ) . COR . 1. In the same or equal circles , sectors that have equal centre angles , equal chords , or equal arcs , are con- gruent . COR . 2. Two diameters that are perpendicular to each 38 [ Book II . ELEMENTS OF GEOMETRY .
... ( part 2 ) . COR . 1. In the same or equal circles , sectors that have equal centre angles , equal chords , or equal arcs , are con- gruent . COR . 2. Two diameters that are perpendicular to each 38 [ Book II . ELEMENTS OF GEOMETRY .
Página 39
... diameters that are perpendicular to each other divide the circle and its circumference into four equal D B · - parts . Each part of the circumference is called a quadrant . COR . 3. Draw the radius OCAB . OC bisects the angle AOB ( I ...
... diameters that are perpendicular to each other divide the circle and its circumference into four equal D B · - parts . Each part of the circumference is called a quadrant . COR . 3. Draw the radius OCAB . OC bisects the angle AOB ( I ...
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.