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Page 154
... , and whether any important part of it was original with Euclid or whether he made any original discoveries in mathematics is a matter of conjecture . BOOK III RATIO , PROPORTION , AND SIMILAR FIGURES 247. 154 PLANE GEOMETRY.
... , and whether any important part of it was original with Euclid or whether he made any original discoveries in mathematics is a matter of conjecture . BOOK III RATIO , PROPORTION , AND SIMILAR FIGURES 247. 154 PLANE GEOMETRY.
Page 155
... ratio , measurement , and proportion , which are really algebraic in character , must be grasped before the strictly geometrical work of Book III can be advantageously taken up . f 248. Ratio . The ratio of one number , a , to a second ...
... ratio , measurement , and proportion , which are really algebraic in character , must be grasped before the strictly geometrical work of Book III can be advantageously taken up . f 248. Ratio . The ratio of one number , a , to a second ...
Page 156
... ratio of 2 to 3 . 8. Separate 154 into three parts in the ratio of 2 : 3 : 6 . 9. The value of a ratio is 3 and the antecedent is 12 less than the consequent . Find the ratio . 250. Measurement . We may speak of the ratio of two con ...
... ratio of 2 to 3 . 8. Separate 154 into three parts in the ratio of 2 : 3 : 6 . 9. The value of a ratio is 3 and the antecedent is 12 less than the consequent . Find the ratio . 250. Measurement . We may speak of the ratio of two con ...
Page 158
... ratio of the first pair equals the ratio of the second pair . This proportion is written either in the form ( 1 ) a : b = c : d or ( 2 ) α b ་ с d The second form is the usual algebraic way of writing an equation in which each member is ...
... ratio of the first pair equals the ratio of the second pair . This proportion is written either in the form ( 1 ) a : b = c : d or ( 2 ) α b ་ с d The second form is the usual algebraic way of writing an equation in which each member is ...
Page 175
... ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent . = = C e d a 816 b + d + f b Given a + c + e To prove that Proof . Let Then a 81 b - α = 018 d - br , - = c = dr , e = fr ...
... ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent . = = C e d a 816 b + d + f b Given a + c + e To prove that Proof . Let Then a 81 b - α = 018 d - br , - = c = dr , e = fr ...
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Common terms and phrases
AABC acute angle adjacent angles adjacent figure algebra altitude angles are equal apothem arc BC Axiom base bisector bisects central angle chord circumference circumscribed common tangent compute congruent Construct a triangle Converse of Theorem convex polygon Corollary cuts decagon diagonals diameter divided Draw drawn equal angles equal circles equal respectively equiangular equilateral triangle equivalent EXERCISES exterior angle Find the area Find the number geometry Given the triangle greater hexagon HINT hypotenuse hypothesis inches inscribed angle intersect isosceles triangle length line-segment locus measured median mid-perpendicular mid-point number of degrees number of sides parallelogram perimeter perpendicular plane Proof proportional prove quadrilateral QUERY radii radius ratio rectangle regular inscribed regular polygon rhombus right angles right triangle secant segments square straight angle straight line tangent third side trapezoid triangle ABC vertex vertices
Popular passages
Page 224 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 182 - If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle...
Page 80 - If two triangles have two sides of 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.
Page 26 - The two pairs of angles 3 and 6, 4 and 5, are called alternate interior angles ; and the two pairs of angles if 1 and 8, 2 and 7, are called alternate exterior angles. The four pairs of angles 1 and 5, 2 and 6, 3 and 7, and 4 and 8 are called corresponding angles.
Page 69 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Page 230 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Page 184 - In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides or legs.
Page 175 - 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 192 - If two chords intersect within a circle, the product of the segments of the one is equal to the product of the segments of the other.
Page 242 - Prove that the area of the square on the hypotenuse of a right triangle equals the sum of the areas of the squares on the other two sides.