## Elements of Geometry and Trigonometry |

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Page 53

AB to be

AB to be

**divided**into equal parts , each of which is less than DO ; there will be at least one point of division between D and O ; let I be that point ; and draw CI . The arcs AB , AI , will be to each other as two whole numbers ... Page 59

By the same construction , each of the halves AE , EB , may be

By the same construction , each of the halves AE , EB , may be

**divided**into two equal parts ; and thus , by successive subdivisions , a given angle , or a given arc may be**divided**into four equal parts , into eight , into sixteen ... Page 71

If AB be

If AB be

**divided**into 7 equal parts , AE will contain 4 of those parts : at each point of division erect a perpendicular to the base ; seven partial rectangles will thus be formed , all equal to each other , because all have the same ... Page 75

... may also be ex2 pressed by EF HI : it is therefore equal to the altitude of the trapezoid multiplied by the line which connects the middle > oints of its inclined sides . PROPOSITION VIII . THEOREM . If a line is

... may also be ex2 pressed by EF HI : it is therefore equal to the altitude of the trapezoid multiplied by the line which connects the middle > oints of its inclined sides . PROPOSITION VIII . THEOREM . If a line is

**divided**BOOK IV . Page 76

If a line is

If a line is

**divided**into two parts , the square described on the whole line is equivalent to the sum of the squares described on the parts , together with twice the rectangle contained by the parts . Let AC be the line , and B the ...### What people are saying - Write a review

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### Common terms and phrases

ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole