Treatise on Plane and Solid Geometry: For Colleges, Schools and Private Students : Written for the Mathematical Course of Joseph RaySargent, Wilson & Hinkle, 1864 - 276 sider |
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Side vi
... ANGLES AT THE CENTER , INTERCEPTED ARCS , POSITIONS OF TWO CIRCUMFERENCES , . CHAPTER V. TRIANGLES . GENERAL PROPERTIES OF TRIANGLES , 52 53 58 59 60 64 72 78 85 EQUALITY OF TRIANGLES , SIMILAR TRIANGLES , • CHAPTER VI vi CONTENTS .
... ANGLES AT THE CENTER , INTERCEPTED ARCS , POSITIONS OF TWO CIRCUMFERENCES , . CHAPTER V. TRIANGLES . GENERAL PROPERTIES OF TRIANGLES , 52 53 58 59 60 64 72 78 85 EQUALITY OF TRIANGLES , SIMILAR TRIANGLES , • CHAPTER VI vi CONTENTS .
Side 48
... intercepted parts of the line AY are equal . 135. Corollary .—- Conversely , if several parallel lines intercept equal segments of a secant , then the several distances between the parallels are equal . 136. Corollary . - When the ...
... intercepted parts of the line AY are equal . 135. Corollary .—- Conversely , if several parallel lines intercept equal segments of a secant , then the several distances between the parallels are equal . 136. Corollary . - When the ...
Side 64
... intercepted arcs . This theorem presents the three following cases : 1st . If the arcs are equal , the angles are equal . For the arcs may be placed one upon the other 64 ELEMENTS OF GEOMETRY . ANGLES AT THE CENTER, INTERCEPTED ARCS,
... intercepted arcs . This theorem presents the three following cases : 1st . If the arcs are equal , the angles are equal . For the arcs may be placed one upon the other 64 ELEMENTS OF GEOMETRY . ANGLES AT THE CENTER, INTERCEPTED ARCS,
Side 65
... intercepted arcs are equal . But BCD is the sum of thirteen , and AOE of five of these equal angles . Therefore , angle BCD angle AOE :: 13 : 5 ; that is , the angles have the same ratio as the arcs . Geom . - 6 3d . It remains to be ...
... intercepted arcs are equal . But BCD is the sum of thirteen , and AOE of five of these equal angles . Therefore , angle BCD angle AOE :: 13 : 5 ; that is , the angles have the same ratio as the arcs . Geom . - 6 3d . It remains to be ...
Side 69
... intercepted arcs have the same ratio as their angles at the center . METHOD OF INFINITES . 203. Modern geometers have made much use of a kind of reasoning which may be called the method of infinites . It consists in supposing that any ...
... intercepted arcs have the same ratio as their angles at the center . METHOD OF INFINITES . 203. Modern geometers have made much use of a kind of reasoning which may be called the method of infinites . It consists in supposing that any ...
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Treatise on Plane and Solid Geometry for Colleges, Schools, and Private Students Eli Todd Tappan Uten tilgangsbegrensning - 1873 |
Treatise on Plane and Solid Geometry: For Colleges, Schools, and Private ... Eli Todd Tappan Ingen forhåndsvisning tilgjengelig - 2017 |
Treatise on Plane and Solid Geometry: For Colleges, Schools, and Private ... Eli Todd Tappan Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
adjacent angles altitude angles are equal angles equal angles formed apothem arc BD bisect called chord circle circumference circumscribed coincide cone Corollary Corollary.-The Corollary.-When demonstration diagonals diameter dicular distance divided edges equal angles equally distant equivalent extend exterior angles faces figure four right angles frustum geometry given angle given line given point given straight line given triangle gles greater Hence homologous lines hypotenuse inscribed inscribed angle intersection isosceles triangle less let fall measured by half number of sides opposite sides parallel lines parallelogram parallelopiped perimeter perpen perpendicular plane polyedral polyedron prism Problem.-To draw PROBLEMS IN DRAWING produced proportional pyramid quadrilateral radii radius ratio rectangle regular polygon respectively equal rhombus right angled triangle secant similar triangles similarly arranged slant hight sphere spherical square described tangent tetraedrons theorem Theorem.-The triangle ABC triangles are equal triedral vertex vertices
Populære avsnitt
Side 98 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Side 52 - 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.
Side 141 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Side 263 - The area of the surface of a sphere is equal to the area of the...
Side 258 - 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...
Side 137 - The squa/re described on the difference of two straight lines is equivalent to the sum of the squares described on the two lines, diminished by twice the rectangle contained by the lines.
Side 227 - ... the two planes are equal polygons. Each side of one of the sections is parallel to the corresponding side of the other section, since they are the intersections of two parallel planes by a third. Hence, that portion of each side of the prism which is between the secant planes, is a parallelogram. Since the sections have their sides respectively equal and parallel, their angles are respectively equal. Therefore, the polygons are equal. 674. Corollary — The section of a prism made by a plane...
Side 237 - The volume of any prism is equal to the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude of the prism DA'.
Side 191 - Theorem. — The intersections of two parallel planes by a third plane are parallel lines. Let AB and CD be the intersections of the two parallel planes M and N, with the plane P.
Side 251 - Every section of a sphere, made by a plane, is a circle, Let AMB be a section, made by a plane, in the sphere whose centre is C.