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 41
... bisects an angle is equidistant from the sides of the angle . Let BCD be the given angle , and AC the bisecting line . Then the distance of the two sides from any point A of that line is meas- ured by perpendiculars to the sides as , AF ...
... bisects an angle is equidistant from the sides of the angle . Let BCD be the given angle , and AC the bisecting line . Then the distance of the two sides from any point A of that line is meas- ured by perpendiculars to the sides as , AF ...
Σελίδα 54
... bisects the circumfer- ence and the circle . For that part upon one side of the diameter may be turned upon that line as its axis . When the two parts thus meet , they will coincide ; for if they did not , some points of the ...
... bisects the circumfer- ence and the circle . For that part upon one side of the diameter may be turned upon that line as its axis . When the two parts thus meet , they will coincide ; for if they did not , some points of the ...
Σελίδα 56
... bisect a given straight line . With A and B as centers , and with a radius greater than the half of AB , describe arcs which intersect in the two points D and E. The straight line joining these two points will 56 ELEMENTS OF GEOMETRY .
... bisect a given straight line . With A and B as centers , and with a radius greater than the half of AB , describe arcs which intersect in the two points D and E. The straight line joining these two points will 56 ELEMENTS OF GEOMETRY .
Σελίδα 57
... bisect AB at C. Let the demonstration be given by the student ( 109 and 151 ) . 172. Problem . — To erect a perpendicular on a given straight line at a given point . Take two points in the line , one on each side of the given point , at ...
... bisect AB at C. Let the demonstration be given by the student ( 109 and 151 ) . 172. Problem . — To erect a perpendicular on a given straight line at a given point . Take two points in the line , one on each side of the given point , at ...
Σελίδα 60
... always means the smaller of the two , unless otherwise expressed . 187. Theorem . — The radius which is perpendicular to a chord bisects the chord and its arc . Let CD be perpendicular at E to the chord AB 60 ELEMENTS OF GEOMETRY . CHORDS,
... always means the smaller of the two , unless otherwise expressed . 187. Theorem . — The radius which is perpendicular to a chord bisects the chord and its arc . Let CD be perpendicular at E to the chord AB 60 ELEMENTS OF GEOMETRY . CHORDS,
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.