Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 σελίδες |
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Αποτελέσματα 1 - 5 από τα 61.
Σελίδα 6
... perpendicular to each other ; as OB ' is perpendicular to OA , which may be expressed by the sign OB ' OA ; also OA LOB ' . B DEF . 5. In all other positions , OB is called an oblique B / A line ; and the angles it forms with OA ...
... perpendicular to each other ; as OB ' is perpendicular to OA , which may be expressed by the sign OB ' OA ; also OA LOB ' . B DEF . 5. In all other positions , OB is called an oblique B / A line ; and the angles it forms with OA ...
Σελίδα 11
... perpendicular to one of two parallels , it is perpendicular to the other also . SCHOLIUM . When the secant cuts the parallels obliquely , there are formed four equal acute angles and four equal obtuse angles . EXERCISE . Prove ≤5 + 7 ...
... perpendicular to one of two parallels , it is perpendicular to the other also . SCHOLIUM . When the secant cuts the parallels obliquely , there are formed four equal acute angles and four equal obtuse angles . EXERCISE . Prove ≤5 + 7 ...
Σελίδα 12
... perpendicular to EF , 28 , being right angles : hence two lines that are perpen- dicular to a third line are parallel to each other . COR . 2. When ≤ 6 + 8 < 2R , it is evident that the lines AB and CD converge to the right : hence two ...
... perpendicular to EF , 28 , being right angles : hence two lines that are perpen- dicular to a third line are parallel to each other . COR . 2. When ≤ 6 + 8 < 2R , it is evident that the lines AB and CD converge to the right : hence two ...
Σελίδα 13
... 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. Prolong BE and CD until they cut in the point O. Prove that ≤ BOC + BAC = 2 R. POLYGONS . XIV ...
... 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. Prolong BE and CD until they cut in the point O. Prove that ≤ BOC + BAC = 2 R. POLYGONS . XIV ...
Σελίδα 20
... , and the middle of the opposite side , bisects the angle , and is perpendicular to the side . COR . 2. Every equilateral triangle is equiangular . XXVI . Theorem . Conversely , if two angles of 20 [ BOOK I. ELEMENTS OF GEOMETRY .
... , and the middle of the opposite side , bisects the angle , and is perpendicular to the side . COR . 2. Every equilateral triangle is equiangular . XXVI . Theorem . Conversely , if two angles of 20 [ BOOK I. ELEMENTS OF GEOMETRY .
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.