Elements of Geometry |
From inside the book
Results 1-5 of 67
Page 22
... radius or semidiameter , and every straight line , as AB , which passes through the centre and is terminated each way by the circumference , is called a diameter . By the definition of a circle the radii are all equal , and all the ...
... radius or semidiameter , and every straight line , as AB , which passes through the centre and is terminated each way by the circumference , is called a diameter . By the definition of a circle the radii are all equal , and all the ...
Page 24
... radius CD will fall upon the radius OG , and the point D upon G , therefore the arc AMD is equal to the arc ENG . = THEOREM . 103. In the same circle , or in equal circles , the greater arc is subtended by the greater chord ; and ...
... radius CD will fall upon the radius OG , and the point D upon G , therefore the arc AMD is equal to the arc ENG . = THEOREM . 103. In the same circle , or in equal circles , the greater arc is subtended by the greater chord ; and ...
Page 25
... radius CG ( fig . 51 ) , perpendicular to a chord AB , Fig . 51 . bisects this chord and the arc subtended by it AGB . Demonstration . Draw the radii CA , CB ; these radii are , with respect to the perpendicular CD , two equal oblique ...
... radius CG ( fig . 51 ) , perpendicular to a chord AB , Fig . 51 . bisects this chord and the arc subtended by it AGB . Demonstration . Draw the radii CA , CB ; these radii are , with respect to the perpendicular CD , two equal oblique ...
Page 26
... 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 to show , that ...
... 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 to show , that ...
Page 27
... radius AC , is a tangent to the circumference . Demonstration . Since every oblique line CE is greater than the ... radius CA , and with respect to this new tangent the radius CA would be an oblique line , and the perpendicular let fall ...
... radius AC , is a tangent to the circumference . Demonstration . Since every oblique line CE is greater than the ... radius CA , and with respect to this new tangent the radius CA would be an oblique line , and the perpendicular let fall ...
Other editions - View all
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...