The Essentials of Geometry (plane)D.C. Heath & Company, 1898 - 242 σελίδες |
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Σελίδα
... from teachers in all parts of the country , which have added materially to the value of the work . WEBSTER WELLS . MASSACHUSETTS INSTITUTE OF TECHNOLOGY , 1898 . • CONTENTS . PRELIMINARY DEFINITIONS PLANE GEOMETRY . Book I. PREFACE .
... from teachers in all parts of the country , which have added materially to the value of the work . WEBSTER WELLS . MASSACHUSETTS INSTITUTE OF TECHNOLOGY , 1898 . • CONTENTS . PRELIMINARY DEFINITIONS PLANE GEOMETRY . Book I. PREFACE .
Σελίδα 88
... value of √2 can only be obtained approximately as a decimal , it is evident that no line , however small , can be found which is contained an integral number of times in each line . Then AB and CD are incommensurable . 182. Although a ...
... value of √2 can only be obtained approximately as a decimal , it is evident that no line , however small , can be found which is contained an integral number of times in each line . Then AB and CD are incommensurable . 182. Although a ...
Σελίδα 89
... values . 185. A constant is a quantity which remains unchanged throughout the same discussion . 186. A limit of a variable is a constant quantity , the dif- ference between which and the variable may be made less than any assigned ...
... values . 185. A constant is a quantity which remains unchanged throughout the same discussion . 186. A limit of a variable is a constant quantity , the dif- ference between which and the variable may be made less than any assigned ...
Σελίδα 90
... values > AC , while vari- able A'M ' is restricted to values < AC ; which is con- trary to the hypothesis that the variables are always equal . Hence , AB cannot be > A'B ' . In like manner , it may be proved that AB cannot be < A'B ...
... values > AC , while vari- able A'M ' is restricted to values < AC ; which is con- trary to the hypothesis that the variables are always equal . Hence , AB cannot be > A'B ' . In like manner , it may be proved that AB cannot be < A'B ...
Σελίδα 110
... BAD = 2 A ' . ( § 208 ) On AD take AC = n , and draw line BC . Then , ABC is the required A. 212. Sch . The problem is possible for any values of the given parts . PROP . XXXVI . PROBLEM . 213. Given a side 110 PLANE GEOMETRY . - BOOK II .
... BAD = 2 A ' . ( § 208 ) On AD take AC = n , and draw line BC . Then , ABC is the required A. 212. Sch . The problem is possible for any values of the given parts . PROP . XXXVI . PROBLEM . 213. Given a side 110 PLANE GEOMETRY . - BOOK II .
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² AC and BC AC² adjacent angles altitude angles are equal apothem approach the limit arc BC base and altitude BC² bisector bisects CD² centre chord circumference circumscribed construct the triangle Converse of Prop decagon diagonals diameter Draw line EFGH equal angles equal respectively equally distant equiangular polygon equilateral triangle equivalent exterior angle figure Given line given point given square homologous sides hypotenuse isosceles triangle line CD line joining measured by arc middle point non-parallel sides number of sides opposite sides parallel parallelogram perimeter perpendicular points of sides polygons AC produced Prove Proof quadrilateral radii radius ratio rectangle regular inscribed regular polygon rhombus right angles right triangle secant segment side BC similar triangles subtended tangent THEOREM transversal trapezoid triangle is equal vertex ZAOB
Δημοφιλή αποσπάσματα
Σελίδα 73 - A chord is a straight line joining the extremities of an arc ; as AB.
Σελίδα 124 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Σελίδα 122 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
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 224 - The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of the perpendiculars.
Σελίδα 40 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 38 - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Σελίδα 192 - 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 193 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.
Σελίδα 142 - In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.