Elements of Geometry |
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Page 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 ...
Page 22
... chord or subtense of an arc is the straight line FG , which joins its extremities ** . 93. A segment of a circle is the portion comprehended be- tween an arc and its chord . 94. 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 ** . 93. A segment of a circle is the portion comprehended be- tween an arc and its chord . 94. A sector is the part of a circle comprehended between an ...
Page 23
... chord is less than the diameter . Demonstration . If the radii CA , CD ( fig . 49 ) , be drawn Fig . 49 . from the centre to the extremities of the chord AD , we shall have the straight line AD < AC + CD , that is , AD < AB ( 91 ) . 100 ...
... chord is less than the diameter . Demonstration . If the radii CA , CD ( fig . 49 ) , be drawn Fig . 49 . from the centre to the extremities of the chord AD , we shall have the straight line AD < AC + CD , that is , AD < AB ( 91 ) . 100 ...
Page 24
... 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 diameter ...
... 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 diameter ...
Page 25
... 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 ...
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Common terms and phrases
ABCD adjacent angles algebraic algebraic quantities altitude angle ACB base centre chord circ circle circular sector circumference coefficient common divisor cone consequently contains Corollary cube cylinder Demonstration denominator denoted diameter divided dividend division equal equivalent evident example exponent expression factors figure fraction frustum given gives greater greatest common divisor homologous sides inscribed less letters logarithm manner measure multiplied obtain parallel parallelogram parallelopiped perpendicular plane MN polyedron preceding prism proportion proposed equation proposition quotient radical sign radii radius ratio rectangle reduced regular polygon remainder result right angles Scholium side BC similar solid angle sphere spherical square root straight line substitute subtract suppose term THEOREM third tion triangle ABC triangular pyramids unity unknown quantity vertex whence
Popular passages
Page 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 7 - 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.
Page 151 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Page 76 - 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.
Page 25 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Page 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Page 160 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Page 203 - In every triangle the sum of the three angles is equal to two right angles.
Page 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Page 141 - If a pyramid is cut by a plane parallel to its base, the...