Elements of GeometryGinn and Heath, 1881 - 250 σελίδες |
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Σελίδα iv
... corollaries . The reason for this is the great diffi- culty of convincing the average student that any importance should be attached to a corollary . Original exercises , however , have been given , not too numerous or too difficult to ...
... corollaries . The reason for this is the great diffi- culty of convincing the average student that any importance should be attached to a corollary . Original exercises , however , have been given , not too numerous or too difficult to ...
Σελίδα 13
... Corollary is a truth easily deduced from the proposition to which it is attached . 44. DEF . A Scholium is a remark upon some particular fea- ture of a proposition . 45. DEF . An Hypothesis is a supposition made in the enunciation of a ...
... Corollary is a truth easily deduced from the proposition to which it is attached . 44. DEF . A Scholium is a remark upon some particular fea- ture of a proposition . 45. DEF . An Hypothesis is a supposition made in the enunciation of a ...
Σελίδα 14
... corollary . Q. E. D. quod erat demonstran- dum . Q. E. F. quod erat faciendum . Adj . adjacent . Ext . - int . exterior - interior . Alt . - int . alternate - interior . Iden . identical . Cons . construction . Sup . supplementary . Sup ...
... corollary . Q. E. D. quod erat demonstran- dum . Q. E. F. quod erat faciendum . Adj . adjacent . Ext . - int . exterior - interior . Alt . - int . alternate - interior . Iden . identical . Cons . construction . Sup . supplementary . Sup ...
Σελίδα 15
... COROLLARY . If two straight lines cut one another , the four angles which they make at the point of intersection are together equal to four right angles . PROPOSITION II . THEOREM . 51. When the sum of PERPENDICULAR AND OBLIQUE LINES ...
... COROLLARY . If two straight lines cut one another , the four angles which they make at the point of intersection are together equal to four right angles . PROPOSITION II . THEOREM . 51. When the sum of PERPENDICULAR AND OBLIQUE LINES ...
Σελίδα 20
... COROLLARY . Only two equal straight lines can be drawn from a point to a straight line ; and of two unequal lines , the greater cuts off the greater distance from the foot of the perpen- dicular . PROPOSITION VII . THEOREM . 57. Two ...
... COROLLARY . Only two equal straight lines can be drawn from a point to a straight line ; and of two unequal lines , the greater cuts off the greater distance from the foot of the perpen- dicular . PROPOSITION VII . THEOREM . 57. Two ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C D AABC AACB AB² ABCD adjacent angles apothem arc A B base and altitude BC² centre centre of symmetry circumference circumscribed construct a square COROLLARY decagon diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular equiangular polygon equilateral equilateral polygon exterior angles figure given circle given line given polygon given square homologous sides hypotenuse intersecting isosceles Let A B Let ABC line A B measured by arc middle point number of sides parallelogram perpendicular plane polygon ABC polygon similar PROBLEM prove Q. E. D. PROPOSITION quadrilateral radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct right angles right triangle SCHOLIUM segment semicircle similar polygons subtend symmetrical with respect tangent THEOREM triangle ABC vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Σελίδα 136 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Σελίδα 207 - Construct a rectangle having the difference of its base and altitude equal to a given line, and its area equivalent to the sum of a given triangle and a given pentagon.
Σελίδα 202 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 142 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Σελίδα 175 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 72 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle.
Σελίδα 73 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Σελίδα 146 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.