The Essentials of GeometryD.C. Heath & Company, 1899 - 395 σελίδες |
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Αποτελέσματα 1 - 5 από τα 41.
Σελίδα 13
... extremities of the line . II . Any point without the perpendicular is unequally dis- tant from the extremities of the line . IC E A D B I. Given line CD 1 to line AB at its middle point D , E any point in CD , and lines AE and BE . To ...
... extremities of the line . II . Any point without the perpendicular is unequally dis- tant from the extremities of the line . IC E A D B I. Given line CD 1 to line AB at its middle point D , E any point in CD , and lines AE and BE . To ...
Σελίδα 14
... extremities of the line . ] ( § 41 , I ) Substituting for BE its equal AE , we have AE + EF > BF , or AF > BF . 42 Cor . I. Every point which is equally distant from the extremities of a straight line , lies in the perpendicular erected ...
... extremities of the line . ] ( § 41 , I ) Substituting for BE its equal AE , we have AE + EF > BF , or AF > BF . 42 Cor . I. Every point which is equally distant from the extremities of a straight line , lies in the perpendicular erected ...
Σελίδα 15
... extremities of a str . line from any point in the erected at its middle point , they make equal △ with the 1. ] CED is a rt . Z ; :: ≤ CED + ≤ C'ED But by hyp . , Then line CEC " is a str . line . ( § 44 ) then , ≤ C'ED is a rt ...
... extremities of a str . line from any point in the erected at its middle point , they make equal △ with the 1. ] CED is a rt . Z ; :: ≤ CED + ≤ C'ED But by hyp . , Then line CEC " is a str . line . ( § 44 ) then , ≤ C'ED is a rt ...
Σελίδα 16
... extremities of the line . ] But CD + DC ' < CE + EC ' . [ A str . line is the shortest line between two points . ] ( § 41 ) ( Ax 4. ) Substituting for DC ' and EC " their equals CD and CE , respectively , we have 2 CD < 2 CE . .. CD ...
... extremities of the line . ] But CD + DC ' < CE + EC ' . [ A str . line is the shortest line between two points . ] ( § 41 ) ( Ax 4. ) Substituting for DC ' and EC " their equals CD and CE , respectively , we have 2 CD < 2 CE . .. CD ...
Σελίδα 17
... extremities of a straight line , their sum is greater than the sum of two other lines similarly drawn , but enveloped by them . E B C Given lines AB and AC drawn from point A to the extremities of line BC ; and DB and DC two other lines ...
... extremities of a straight line , their sum is greater than the sum of two other lines similarly drawn , but enveloped by them . E B C Given lines AB and AC drawn from point A to the extremities of line BC ; and DB and DC two other lines ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² adjacent angles altitude apothem approach the limit axis base and altitude BC² bisector bisects centre chord circle circumference circumscribed coincide cone of revolution Converse of Prop diagonals diameter diedral angle distance Draw line equal respectively equally distant equilateral equivalent exterior angle faces Find the area frustum Given line given point Hence homologous homologous sides hypotenuse intersecting isosceles triangle lateral area lateral edges line drawn line joining middle point number of sides parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedral polyedron prism Prove pyramid quadrilateral radii radius rectangle regular inscribed regular polygon rhombus right angles right triangle segment side BC similar slant height spherical polygon spherical triangle square tangent tetraedron THEOREM trapezoid triangle ABC triangular prism triedral vertex vertices volume Whence
Δημοφιλή αποσπάσματα
Σελίδα 58 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Σελίδα 322 - A right circular cylinder may be generated by the revolution of a rectangle about one of its sides as an axis.
Σελίδα 371 - A zone is a portion of the surface of a sphere included between two parallel planes.
Σελίδα 49 - ... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if...
Σελίδα 336 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...
Σελίδα 151 - If one leg of a right triangle is double the other, the perpendicular from the vertex of the right angle to the hypotenuse divides it into segments which are to each other as 1 to 4.
Σελίδα 328 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 205 - S' denote the areas of two © whose radii are R and R', and diameters D and D', respectively. Then, | = "* § = ££ = £• <§337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.
Σελίδα 73 - A chord is a straight line joining the extremities of an arc ; as AB.
Σελίδα 202 - The circumferences of two circles are to each other as their radii. Given C and C" the circumferences of two © whose radii are R and R', respectively.