Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 σελίδες |
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Σελίδα 22
... centre . The circle is the space terminated by this curved line * . 91. Every straight line CA , CE , CD ( fig . 46 ) , & c . , drawn from the centre to the circumference is called a radius or semidiameter , and every straight line , as ...
... centre . The circle is the space terminated by this curved line * . 91. Every straight line CA , CE , CD ( fig . 46 ) , & c . , drawn from the centre to the circumference is called a radius or semidiameter , and every straight line , as ...
Σελίδα 23
... centre , which is contrary to the definition of a circle . THEOREM . 99. Every 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 ...
... centre , which is contrary to the definition of a circle . THEOREM . 99. Every 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 ...
Σελίδα 25
... centre , and the middle , of the arc subtended by that chord . For this perpendicular is the same as that let fall from the centre upon the same chord , since they both pass through the middle of the chord ( 51 ) . THEOREM . 107. The ...
... centre , and the middle , of the arc subtended by that chord . For this perpendicular is the same as that let fall from the centre upon the same chord , since they both pass through the middle of the chord ( 51 ) . THEOREM . 107. The ...
Σελίδα 26
... centre O with the radius OB , will pass through the three points A , B , C. It is thus proved , that the circumference of a circle may be made to pass through any three given points , which are not in the same straight line ; it remains ...
... centre O with the radius OB , will pass through the three points A , B , C. It is thus proved , that the circumference of a circle may be made to pass through any three given points , which are not in the same straight line ; it remains ...
Σελίδα 27
... centre , and of two unequal chords the less is at the greater aistance from the centre . Demonstration 1. Let the chord AB = DE ( fig . 53 ) . Bisect Fig . 53 . these chords by the perpendiculars CF , CG , and draw the radii CA , CD ...
... centre , and of two unequal chords the less is at the greater aistance from the centre . Demonstration 1. Let the chord AB = DE ( fig . 53 ) . Bisect Fig . 53 . these chords by the perpendiculars CF , CG , and draw the radii CA , CD ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Σελίδα 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.
Σελίδα 203 - In every triangle the sum of the three angles is equal to two right angles.
Σελίδα 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Σελίδα 141 - If a pyramid is cut by a plane parallel to its base, the...