Treatise on Plane and Solid Geometry: For Colleges, Schools and Private Students : Written for the Mathematical Course of Joseph RaySargent, Wilson & Hinkle, 1864 - 276 σελίδες |
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Σελίδα 29
... contain the less . A line may thus be produced any required length . 71. The student must distinguish between the problems of geometry and problems in drawing . The former state what can be done with pure geometrical magnitudes , and ...
... contain the less . A line may thus be produced any required length . 71. The student must distinguish between the problems of geometry and problems in drawing . The former state what can be done with pure geometrical magnitudes , and ...
Σελίδα 30
... of times that b is contained in the least common multiple of the two lines , and y the number of times it contains c . Then x times b is equal to y times c . Therefore , from a point A , draw an indefinite 30 ELEMENTS OF GEOMETRY .
... of times that b is contained in the least common multiple of the two lines , and y the number of times it contains c . Then x times b is equal to y times c . Therefore , from a point A , draw an indefinite 30 ELEMENTS OF GEOMETRY .
Σελίδα 74
... contain the angle . Thus , the angle AEI is inscribed in the arc AEI , and the arc AEI con- tains the angle AEI . E I An angle is said to stand upon the arc intercepted between its sides . Thus , the angle AEI stands upon the arc AOI ...
... contain the angle . Thus , the angle AEI is inscribed in the arc AEI , and the arc AEI con- tains the angle AEI . E I An angle is said to stand upon the arc intercepted between its sides . Thus , the angle AEI stands upon the arc AOI ...
Σελίδα 78
... contain a given angle . H G Let AB be the chord , and C the angle . Make the angle DAB equal to C. At A erect a ... contained in the arc AHGB is also measured by half of the same arc ( 222 ) , and is therefore equal to BAD , which ...
... contain a given angle . H G Let AB be the chord , and C the angle . Make the angle DAB equal to C. At A erect a ... contained in the arc AHGB is also measured by half of the same arc ( 222 ) , and is therefore equal to BAD , which ...
Σελίδα 84
... contained by the tangents is double the angle contained by the line joining the points of contact and the radius extending to one of them . 23. If from the ends of a diameter perpendiculars be let fall on any line cutting the ...
... contained by the tangents is double the angle contained by the line joining the points of contact and the radius extending to one of them . 23. If from the ends of a diameter perpendiculars be let fall on any line cutting the ...
Άλλες εκδόσεις - Προβολή όλων
Treatise on Plane and Solid Geometry: For Colleges, Schools, and Private ... Eli Todd Tappan Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Treatise on Plane and Solid Geometry: For Colleges, Schools, and Private ... Eli Todd Tappan Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 263 - The area of the surface of a sphere is equal to the area of the...
Σελίδα 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...
Σελίδα 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.
Σελίδα 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...
Σελίδα 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'.
Σελίδα 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.
Σελίδα 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.