A new supplement to Euclid's Elements of geometry, by the author of 'A new introduction to the mathematics'. |
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Page 12
... one - third of two right - angles ; that is , to two - thirds of the right - angle acb ; wherefore the remaining angle acd is one - third of the right - angle acb ; and the angle bcd being bisected in ce , the three angles acd , dce ...
... one - third of two right - angles ; that is , to two - thirds of the right - angle acb ; wherefore the remaining angle acd is one - third of the right - angle acb ; and the angle bcd being bisected in ce , the three angles acd , dce ...
Page 24
... 1 Euclid ) ; wherefore the triangle acb is isosceles , and the angles cab , cba , at the base ab are equal ( 1 Eu ... one - third of two right - angles . - 1200 2 And because the base or chord ab is bisected in the point e , ergo ( by ...
... 1 Euclid ) ; wherefore the triangle acb is isosceles , and the angles cab , cba , at the base ab are equal ( 1 Eu ... one - third of two right - angles . - 1200 2 And because the base or chord ab is bisected in the point e , ergo ( by ...
Page 42
... one - third of the radius ac ; wherefore the arc fgh is one - third of the arc adib ; but the arc ad is equal to the arc fgh ( by the con- struction ) , wherefore the arc ad is one - third of the arc adib . And because arcs in equal ...
... one - third of the radius ac ; wherefore the arc fgh is one - third of the arc adib ; but the arc ad is equal to the arc fgh ( by the con- struction ) , wherefore the arc ad is one - third of the arc adib . And because arcs in equal ...
Page 47
... one of the sides of the inscribed square , the square described upon the diameter ae is equal to the square abcd ... third of the given circle . Let abc be the given circle , of which ac is the diameter ; it is required to cut off from it a ...
... one of the sides of the inscribed square , the square described upon the diameter ae is equal to the square abcd ... third of the given circle . Let abc be the given circle , of which ac is the diameter ; it is required to cut off from it a ...
Page 48
... one of the sides ad ; bisect ae in the point ƒ , and from f , as a centre at the distance af , describe the circle aeg ; Then will the circle aeg be one - third of the circle abc . Because the angle adc contains 120 ° , and that the ...
... one of the sides ad ; bisect ae in the point ƒ , and from f , as a centre at the distance af , describe the circle aeg ; Then will the circle aeg be one - third of the circle abc . Because the angle adc contains 120 ° , and that the ...
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A New Supplement to Euclid's Elements of Geometry, by the Author of 'a New ... Joseph Denison No preview available - 2015 |
Common terms and phrases
ae is equal angle abc angle acb angle bad angles cab arc adc bisected centre circle abcd circle age circle klmn clid contains 30 Corollary demonstrated describe a square describe the circle describe the square diagonal diameter ac double the square duplicate ratio equal angles equal sides equal to 60 equal to half equi equilateral triangle given circle abd given circle efgh given line given right line given square abcd half the given hexagon homologous sides hypothenuse isosceles triangle join Let abcd multiple octuple Proposition 14 quadruple the square radii radius ac rectangles ac remaining angle right-angle acb Scholium sextuple side ab side ac similar polygon inscribed similar triangles spaces described square abfg square bdih square described square efgh square gikl square of ac subtend Supplement triangle abc trigon abc trigon inscribed triple the square trisected vertical angle wherefore the angle wherefore the square
Popular passages
Page 62 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Page 5 - The areas of two similar triangles are to one another as the squares of their homologous or similarly situated sides (fig.
Page 41 - PROP. XV. THEOR. Magnitudes have the same ratio to one another which their equimultiples have. Let AB be the same multiple of C, that DE is of F: C shall be to F, as AB to DE.
Page 63 - Ratios that are the same to the same ratio, are the same to one another.
Page 39 - F is of B, and that magnitudes have the same ratio to one another which their equimultiples have; (v.
Page 13 - PQ the given straight line, and A the given point in it. It Is required to describe a circle to touch ihe 0 DEB, and also to touch PQ at A.
Page 56 - In any triangle the square on a side opposite to an acute angle is less than the sum of the squares on the sides which contain the acute angle ; (e}. In an obtuse-angled triangle the square on the side subtending the obtuse angle is greater than the sum of the squares on the sides containing...
Page 57 - PROPOSITION 20. In a circle the angle at the centre is double of the angle at the circumference, when the angles have the same circumference as base.
Page 63 - CE equal to the ratio of the square of AB to the square of AD.
Page 61 - And in continued proportions, the square of the mean is equal to the rectangle contained by the extremes.