Elements of GeometryHilliard, Gray,, 1841 - 235 Seiten |
Im Buch
Ergebnisse 1-5 von 33
Seite vi
... chords , of tangents , and of the measure of angles by the arcs of a circle . These two sections are followed by the resolution of certain problems relating to the construction of figures . The third section , entitled the proportions ...
... chords , of tangents , and of the measure of angles by the arcs of a circle . These two sections are followed by the resolution of certain problems relating to the construction of figures . The third section , entitled the proportions ...
Seite 24
... chord or subtense of an arc is the straight line FG , which joins its extremities . † 91. A segment of a circle is the portion comprehended be- tween an arc and its chord . 92. A sector is the part of a circle comprehended between an ...
... chord or subtense of an arc is the straight line FG , which joins its extremities . † 91. A segment of a circle is the portion comprehended be- tween an arc and its chord . 92. A sector is the part of a circle comprehended between an ...
Seite 25
... chord is less than the diameter . Demonstration . If the radii CA , CD ( fig . 49 ) , be drawn from Fig . 49 . the centre to the extremities of the chord AD , we shall have the straight line AD < AC + CD ; that is , AD < AB ( 88 ) . 100 ...
... chord is less than the diameter . Demonstration . If the radii CA , CD ( fig . 49 ) , be drawn from Fig . 49 . the centre to the extremities of the chord AD , we shall have the straight line AD < AC + CD ; that is , AD < AB ( 88 ) . 100 ...
Seite 26
... chords , and , conversely , equal chords subtend equal arcs . Demonstration . The radius AC ( fig . 50 ) being equal to the radius EO , and the arc AMD equal to the arc ENG , the chord AD will be equal to the chord EG . For , the ...
... chords , and , conversely , equal chords subtend equal arcs . Demonstration . The radius AC ( fig . 50 ) being equal to the radius EO , and the arc AMD equal to the arc ENG , the chord AD will be equal to the chord EG . For , the ...
Seite 27
... chord would diminish , and the reverse ; thus , the arc AKBD being greater than AKBH , the chord AD of the first is less than the chord AH of the second . THEOREM . 105. The radius CG ( fig . 51 ) , perpendicular to a chord AB , Fig ...
... chord would diminish , and the reverse ; thus , the arc AKBD being greater than AKBH , the chord AD of the first is less than the chord AH of the second . THEOREM . 105. The radius CG ( fig . 51 ) , perpendicular to a chord AB , Fig ...
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle join less Let ABC let fall Let us suppose line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM third three angles triangle ABC triangular prism triangular pyramids vertex vertices whence
Beliebte Passagen
Seite 67 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Seite 9 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Seite 65 - 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'.
Seite 160 - ABC (fig. 224) be any spherical triangle ; produce the sides AB, AC, till they meet again in D. The arcs ABD, ACD, will be...
Seite 168 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Seite 157 - 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.
Seite 8 - Any side of a triangle is less than the sum of the other two sides...
Seite 82 - 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.
Seite 29 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Seite 182 - CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude.