Elements of GeometryGinn and Heath, 1877 - 250 σελίδες |
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Σελίδα 93
... means that an angle at the centre is such part of the angular magnitude about that point ( four right angles ) as its intercepted arc is of the whole circumference . A circumference is divided into 360 equal arcs , and each arc is ...
... means that an angle at the centre is such part of the angular magnitude about that point ( four right angles ) as its intercepted arc is of the whole circumference . A circumference is divided into 360 equal arcs , and each arc is ...
Σελίδα 128
... . terms . terms . 249. The Extremes in a proportion are the first and fourth 250. The Means in a proportion are the second and third 251. DEF . In the proportion a : b :: PROPORTIONAL LINES AND SIMILAR POLYGONS THEORY OF PROPORTION.
... . terms . terms . 249. The Extremes in a proportion are the first and fourth 250. The Means in a proportion are the second and third 251. DEF . In the proportion a : b :: PROPORTIONAL LINES AND SIMILAR POLYGONS THEORY OF PROPORTION.
Σελίδα 129
... Mean Proportional between a and c . 254. DEF . Four quantities are Reciprocally Proportional when the first is to ... means , or the extremes , are made to exchange places . Thus in the proportion a b c d , we have either dbc : a . a cbd ...
... Mean Proportional between a and c . 254. DEF . Four quantities are Reciprocally Proportional when the first is to ... means , or the extremes , are made to exchange places . Thus in the proportion a b c d , we have either dbc : a . a cbd ...
Σελίδα 131
... mean proportional between two quantities is equal to the square root of their product . In the proportion a bbc , b2 = a c , ( the product of the extremes is equal to the product of the means ) . Whence , extracting the square root , b ...
... mean proportional between two quantities is equal to the square root of their product . In the proportion a bbc , b2 = a c , ( the product of the extremes is equal to the product of the means ) . Whence , extracting the square root , b ...
Σελίδα 132
... means . We are to prove Let ad = b c . a : b :: c : d . Divide both members of the given equation by bd . Then α b = с d or , a b c d .. Q. E. D. PROPOSITION IV . 262. If four quantities of the same kind be in propor- tion , they will ...
... means . We are to prove Let ad = b c . a : b :: c : d . Divide both members of the given equation by bd . Then α b = с d or , a b c d .. Q. E. D. PROPOSITION IV . 262. If four quantities of the same kind be in propor- tion , they will ...
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A B C AABC AACB ABCD adjacent angles alt.-int altitude apothem arc A B bisect centre circumference circumscribed coincide COROLLARY describe an arc diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular polygon equilateral equilateral polygon exterior angles figure given line given point given polygon given straight line greater homologous sides hypotenuse isosceles triangle Let A B Let ABC limit line A B measured by arc middle point number of sides parallelogram perimeter perpendicular plane PROBLEM prove Q. E. D. PROPOSITION quadrilateral radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct rhombus right angles right triangle SCHOLIUM segment sides of equal sides of similar similar polygons subtend tangent THEOREM third side triangle ABC variable vertex vertices