Plane and Solid GeometryAmerican Book Company, 1899 - 384 σελίδες |
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Σελίδα 338
... Spherical Angle . 683. A portion of the surface of a sphere bounded by three or more arcs of great circles is called ... Triangle . A spherical triangle is right , oblique , equilateral , isosceles , etc. , under the same conditions that ...
... Spherical Angle . 683. A portion of the surface of a sphere bounded by three or more arcs of great circles is called ... Triangle . A spherical triangle is right , oblique , equilateral , isosceles , etc. , under the same conditions that ...
Σελίδα 340
... spherical triangle are quadrants , the third side measures the angle opposite . 692. Cor . III . If each side of a spherical triangle is a quadrant , each angle is a right angle . 693. Cor . IV . If two arcs of great circles cut each ...
... spherical triangle are quadrants , the third side measures the angle opposite . 692. Cor . III . If each side of a spherical triangle is a quadrant , each angle is a right angle . 693. Cor . IV . If two arcs of great circles cut each ...
Σελίδα 341
... spherical triangle is greater than the difference of the other two sides . Proposition X 698. Form a sphere and draw on it a spherical polygon ; pass planes through the sides of the polygon and the center of the sphere , and thus cut ...
... spherical triangle is greater than the difference of the other two sides . Proposition X 698. Form a sphere and draw on it a spherical polygon ; pass planes through the sides of the polygon and the center of the sphere , and thus cut ...
Σελίδα 342
... triangle of ABC . If from A , B , and C as poles entire great circles instead of arcs are described , these circles will divide the surface of the sphere into eight spherical triangles . B A ' Of these eight triangles , that one is the ...
... triangle of ABC . If from A , B , and C as poles entire great circles instead of arcs are described , these circles will divide the surface of the sphere into eight spherical triangles . B A ' Of these eight triangles , that one is the ...
Σελίδα 343
William James Milne. Proposition XII 701. On the surface of a sphere , draw a spherical triangle and its polar triangle ; select an angle of one of these and extend its sides , if necessary , to meet the opposite side of the other triangle ...
William James Milne. Proposition XII 701. On the surface of a sphere , draw a spherical triangle and its polar triangle ; select an angle of one of these and extend its sides , if necessary , to meet the opposite side of the other triangle ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles altitude angle formed angles are equal angles compare apothem arc intercepted base bisector bisects called central angle chord circle whose center circumference circumscribed compare in length Construct a triangle cylinder Data diagonals diameter dihedral angles distance divided equal circles equidistant equilateral triangle equivalent exterior angle extremities FGHJK Find the locus frustum given line given point given straight line Hence homologous sides hypotenuse inscribed angle intersecting isosceles trapezoid isosceles triangle measured by arc middle point number of sides opposite sides parallel lines parallelogram parallelopiped pass perimeter perpendicular plane polyhedron prism produced Proof prove pyramid Q.E.D. Proposition quadrilateral radii radius ratio rect rectangle formed regular polygon respectively rhombus right angle right triangle secant segments sphere spherical triangle subtended surface tangent Theorem transversal trapezoid triangle ABC triangles are equal trihedral vertex vertical angle volume
Δημοφιλή αποσπάσματα
Σελίδα 67 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Σελίδα 47 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Σελίδα 64 - From 56 and 57 the pupils should learn that two triangles are equal in every respect (a) when two sides and the included angle of one are equal to two sides and the included angle of the other...
Σελίδα 33 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.
Σελίδα 219 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Σελίδα 217 - The. sum of the angles of any polygon is equal to twice as many right angles as the polygon has sides, less four right angles.
Σελίδα 136 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.
Σελίδα 90 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.
Σελίδα 374 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Σελίδα 176 - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.