Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 páginas |
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Página 18
... time in the two lines , B'A ' and C'A ' , must fall at their intersection , A ' , and the two triangles coincide throughout ; or A ABC A'B'C ' . XXII . Theorem . If two triangles have two sides 18 [ BOOK I ELEMENTS OF GEOMETRY .
... time in the two lines , B'A ' and C'A ' , must fall at their intersection , A ' , and the two triangles coincide throughout ; or A ABC A'B'C ' . XXII . Theorem . If two triangles have two sides 18 [ BOOK I ELEMENTS OF GEOMETRY .
Página 36
... intersection , F , is equally distant from A , B , and C , and is the only point . Hence the circumference drawn from the centre , F , with a radius FA = FB = FC , will pass through the points A , B , and C , and is the only one that ...
... intersection , F , is equally distant from A , B , and C , and is the only point . Hence the circumference drawn from the centre , F , with a radius FA = FB = FC , will pass through the points A , B , and C , and is the only one that ...
Página 48
... intersect each other , their angle has the same numerical measure as half the algebraic difference of the in- cluded arcs of any circumference which they cut . RELATIVE POSITION OF CIRCLES . XIV . Theorem . If two circumferences intersect ...
... intersect each other , their angle has the same numerical measure as half the algebraic difference of the in- cluded arcs of any circumference which they cut . RELATIVE POSITION OF CIRCLES . XIV . Theorem . If two circumferences intersect ...
Página 58
... intersect in a point , D ; and ABDC is the parallelogram required . XXXII . Problem . To describe a circumference that shall pass through three given points not in the same straight line . Problem . To find the centre of a given ...
... intersect in a point , D ; and ABDC is the parallelogram required . XXXII . Problem . To describe a circumference that shall pass through three given points not in the same straight line . Problem . To find the centre of a given ...
Página 59
... intersect each other , four circles may be drawn tangent to them ; also each intersecting point , A , is in the same straight line with the centres , two and two ; thus , D'AD " and ADD " " are straight lines . ( I. , 32. ) ' D ...
... intersect each other , four circles may be drawn tangent to them ; also each intersecting point , A , is in the same straight line with the centres , two and two ; thus , D'AD " and ADD " " are straight lines . ( I. , 32. ) ' D ...
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.