Plane Geometry |
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Page 92
... ratio . In other words the ratio of two quantities of the same kind is the ratio of their numeri- cal measures expressed in terms of a common unit . The ratio of a to b is written ab , or α b 268. Two quantities that can be expressed in ...
... ratio . In other words the ratio of two quantities of the same kind is the ratio of their numeri- cal measures expressed in terms of a common unit . The ratio of a to b is written ab , or α b 268. Two quantities that can be expressed in ...
Page 93
... ratio can be found within any required degree of accuracy . 270. The ratio of two incommensurable quantities is called an incommensurable ratio ; and is a fixed value which its suc- cessive approximate values constantly approach . THE ...
... ratio can be found within any required degree of accuracy . 270. The ratio of two incommensurable quantities is called an incommensurable ratio ; and is a fixed value which its suc- cessive approximate values constantly approach . THE ...
Page 98
... ratio , and each approaches a limit that is not zero , the limits have the same ratio . Let x and y be two variables , a and b their respective limits . Let x = r , a constant ; then x = ry . y Since x and ry are two variables that are ...
... ratio , and each approaches a limit that is not zero , the limits have the same ratio . Let x and y be two variables , a and b their respective limits . Let x = r , a constant ; then x = ry . y Since x and ry are two variables that are ...
Page 99
... ratio of AB and CD . Apply CD to AB as many times as possible . Suppose twice , with a remainder EB . Then apply EB ... ratio of two arcs of the same circle or of equal circles can be found . If the lines or arcs are incommensurable , an ...
... ratio of AB and CD . Apply CD to AB as many times as possible . Suppose twice , with a remainder EB . Then apply EB ... ratio of two arcs of the same circle or of equal circles can be found . If the lines or arcs are incommensurable , an ...
Page 100
... ratio as their intercepted arcs . Β ' m FIG . 1 . FIG . 2 . FIG . 3 . In the equal circles whose centres are C and C ́ , let ACB and A'C'B ' be the angles , AB and A'B ' the intercepted arcs . To prove that LA'C'B ' LACB arc A'B ' arc ...
... ratio as their intercepted arcs . Β ' m FIG . 1 . FIG . 2 . FIG . 3 . In the equal circles whose centres are C and C ́ , let ACB and A'C'B ' be the angles , AB and A'B ' the intercepted arcs . To prove that LA'C'B ' LACB arc A'B ' arc ...
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Common terms and phrases
AB² ABCD AC² acute angle adjacent angles altitude angles are equal apothem arc A'B base bisector bisects called centre chord circumference circumscribed circle coincide decagon diagonals diameter divide Draw equal circles equiangular equiangular polygon equidistant equilateral triangle exterior angle feet Find the area Find the locus given angle given circle given line given point given straight line given triangle greater Hence homologous sides hypotenuse inches inscribed regular intercepted intersecting isosceles trapezoid isosceles triangle legs limit line drawn median middle point number of sides parallelogram perimeter perpendicular plane PROBLEM Proof prove Q. E. D. PROPOSITION quadrilateral radii radius ratio rectangle regular hexagon regular inscribed regular polygon rhombus right angle right triangle secant segments straight angle supplementary tangent THEOREM third side trapezoid triangle ABC triangle is equal variable vertex
Popular passages
Page 33 - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.
Page 150 - If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. In the triangles ABC and A'B'C', let ZA = Z A', and let AB : A'B' = AC : A'C'. To prove that the A ABC and A'B'C
Page 66 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Page 191 - 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. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Page 169 - In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side.
Page 32 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 71 - The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude.
Page 156 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 75 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 162 - The sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.