Elements of Geometry and Conic SectionsHarper & brothers, 1861 - 234 Seiten |
Im Buch
Ergebnisse 1-5 von 30
Seite 7
... Regular Polygons , and the Area of the Circle . SOLID GEOMETRT BOOK VII . Planes and Solid Angles . BOOK VIII . Polyedrons BOOK IX . Spherical Geometry BOOK X. The Three round Bodies . Parabola . Ellipse Hyperbola • CONIC SECTIONS ...
... Regular Polygons , and the Area of the Circle . SOLID GEOMETRT BOOK VII . Planes and Solid Angles . BOOK VIII . Polyedrons BOOK IX . Spherical Geometry BOOK X. The Three round Bodies . Parabola . Ellipse Hyperbola • CONIC SECTIONS ...
Seite 12
... regular deduction . An indirect demonstration shows that any supposition con- trary to the truth advanced , necessarily leads to an absurd- ity . 23. A problem is a question proposed which requires a so lution . 24. A postulate requires ...
... regular deduction . An indirect demonstration shows that any supposition con- trary to the truth advanced , necessarily leads to an absurd- ity . 23. A problem is a question proposed which requires a so lution . 24. A postulate requires ...
Seite 97
... the rectangle CDxCE is equivalent to the square of AC , which is , by construction , equivalent to the given area . Also , the difference of the lines CE , CD is equal to DE or AB . E BOOK VI . REGULAR POLYGONS , AND THE AREA OF BOOK V. 97.
... the rectangle CDxCE is equivalent to the square of AC , which is , by construction , equivalent to the given area . Also , the difference of the lines CE , CD is equal to DE or AB . E BOOK VI . REGULAR POLYGONS , AND THE AREA OF BOOK V. 97.
Seite 98
... regular polygon is one which is both equiangular and equilateral . An equilateral triangle is a regular polygon of three sides ; a square is one of four . PROPOSITION I. THEOREM . Regular polygons of the same number of sides are similar ...
... regular polygon is one which is both equiangular and equilateral . An equilateral triangle is a regular polygon of three sides ; a square is one of four . PROPOSITION I. THEOREM . Regular polygons of the same number of sides are similar ...
Seite 99
... regular polygon are deter mined by the number of its sides . PROPOSITION II . THEOREM . A circle may be described about any regular polygon , and another may be inscribed within it . Let ABCDEF be any regular polygon ; a circle may be ...
... regular polygon are deter mined by the number of its sides . PROPOSITION II . THEOREM . A circle may be described about any regular polygon , and another may be inscribed within it . Let ABCDEF be any regular polygon ; a circle may be ...
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected CA² chord circle circumference cone contained convex surface curve described diagonals diameter draw ellipse equal angles equal to AC equally distant equiangular equilateral equivalent exterior angle foci four right angles frustum given point given straight line greater hyperbola hypothenuse inscribed intersect join latus rectum Let ABC lines AC major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles Prop right-angled triangle Scholium segment side AC similar similar triangles solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Beliebte Passagen
Seite 27 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Seite 157 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Seite 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Seite 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Seite 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 10 - CHG; and they are adjacent angles; but when a straight line standing on another straight line makes the adjacent angles equal to one another, each of them is a right angle; and the straight line which stands upon the other is called a perpendicular to it; therefore from the given point C a perpendicular CH has been drawn to the given straight line AB.
Seite 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 22 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Seite 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Seite 41 - It follows that either couplet of a proportion may be multiplied or divided by any quantity, and the resulting quantities will be in proportion. And since by...