The Essentials of Geometry (plane)D.C. Heath & Company, 1898 - 242 σελίδες |
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Αποτελέσματα 1 - 5 από τα 37.
Σελίδα 7
... Hence , a perpendicular can be drawn to AB at C , and but one . 26. Cor . All right angles are equal . Let ABC and DEF be right angles . To prove angles ABC and DEF equal . IC A B D E Let angle ABC be superposed ( i.e. , placed ) upon ...
... Hence , a perpendicular can be drawn to AB at C , and but one . 26. Cor . All right angles are equal . Let ABC and DEF be right angles . To prove angles ABC and DEF equal . IC A B D E Let angle ABC be superposed ( i.e. , placed ) upon ...
Σελίδα 9
... Hence , the sum of angles ACD and BCD is equal to two right angles . 33. Sch . Since angles ACD and BCD are supplementary ( § 30 ) , the theorem may be stated as follows : If two adjacent angles have their exterior sides in the same ...
... Hence , the sum of angles ACD and BCD is equal to two right angles . 33. Sch . Since angles ACD and BCD are supplementary ( § 30 ) , the theorem may be stated as follows : If two adjacent angles have their exterior sides in the same ...
Σελίδα 11
... Hence , EC coincides with BC , and AC and BC lie in the same str . line . 38. Sch . I. It will be observed that the enunciation of every theorem consists essentially of two parts ; the Hypoth- esis , and the Conclusion . Thus , we may ...
... Hence , EC coincides with BC , and AC and BC lie in the same str . line . 38. Sch . I. It will be observed that the enunciation of every theorem consists essentially of two parts ; the Hypoth- esis , and the Conclusion . Thus , we may ...
Σελίδα 15
... " is a str . line . But one str . line can be drawn between two points . ] Hence , CE cannot be AB , and CD is the only can be drawn . ( Ax . 3 ) that PROP . VII . THEOREM . 46. The perpendicular is RECTILINEAR FIGURES . 15.
... " is a str . line . But one str . line can be drawn between two points . ] Hence , CE cannot be AB , and CD is the only can be drawn . ( Ax . 3 ) that PROP . VII . THEOREM . 46. The perpendicular is RECTILINEAR FIGURES . 15.
Σελίδα 20
... Hence , DE cannot be > DF . ( $ 49 ) In like manner , if we suppose DE < DF , CE would be < CF , which is contrary to the hypothesis that CE CF. Hence , DE cannot be < DF . Then , if DE can be neither > DF , nor < DF , we must have DE ...
... Hence , DE cannot be > DF . ( $ 49 ) In like manner , if we suppose DE < DF , CE would be < CF , which is contrary to the hypothesis that CE CF. Hence , DE cannot be < DF . Then , if DE can be neither > DF , nor < DF , we must have DE ...
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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.