Elements of GeometryGinn and Heath, 1881 - 250 σελίδες |
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Σελίδα 73
... the chord AB , ( Fig . 3 ) , subtends the arc AMB and the arc A D B. Whenever a chord and its arc are spoken of , the less arc is meant unless it be otherwise stated . 167. DEF . A Segment of a circle is a CIRCLES DEFINITIONS.
... the chord AB , ( Fig . 3 ) , subtends the arc AMB and the arc A D B. Whenever a chord and its arc are spoken of , the less arc is meant unless it be otherwise stated . 167. DEF . A Segment of a circle is a CIRCLES DEFINITIONS.
Σελίδα 74
George Albert Wentworth. 167. DEF . A Segment of a circle is a portion of a circle enclosed by an arc and its chord , as A M B , Fig . 1 . 168. DEF . A Semicircle is a segment equal to one half the circle , as A DC , Fig . 1 . 169. DEF ...
George Albert Wentworth. 167. DEF . A Segment of a circle is a portion of a circle enclosed by an arc and its chord , as A M B , Fig . 1 . 168. DEF . A Semicircle is a segment equal to one half the circle , as A DC , Fig . 1 . 169. DEF ...
Σελίδα 75
... segment A M B on A B as an axis until it comes into the plane of AP B , the arc AMB will coincide with the arc APB ; because every point in each is equally dis- tant from the centre 0 . M P B chord . PROPOSITION I. THEOREM . 177. The ...
... segment A M B on A B as an axis until it comes into the plane of AP B , the arc AMB will coincide with the arc APB ; because every point in each is equally dis- tant from the centre 0 . M P B chord . PROPOSITION I. THEOREM . 177. The ...
Σελίδα 95
... segment greater than a semicircle is an acute angle ; for it is measured by an arc less than one - half a semi - circumference ; i . e . by an arc less than 90 ° . 206. COR . 3. An angle inscribed in a segment less than a semicircle is ...
... segment greater than a semicircle is an acute angle ; for it is measured by an arc less than one - half a semi - circumference ; i . e . by an arc less than 90 ° . 206. COR . 3. An angle inscribed in a segment less than a semicircle is ...
Σελίδα 124
... segment which shall contain a given angle . H K E B M 7 ′′ Let AB be the given line , and M the given angle . It is required to describe a segment upon the line A B , which shall contain / M. At the point B construct △ A B E equal to ...
... segment which shall contain a given angle . H K E B M 7 ′′ Let AB be the given line , and M the given angle . It is required to describe a segment upon the line A B , which shall contain / M. At the point B construct △ A B E equal to ...
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'.