A new supplement to Euclid's Elements of geometry, by the author of 'A new introduction to the mathematics'.Whittaker & Company, 1840 - 84 páginas |
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Página 26
... one of the sides of a hexa- gon inscribed in the given circle . Let abd be a trigon inscribed in the given circle abde , and let the line de be one of the sides of a hexagon inscribed in the given circle ; then will 26 A NEW SUPPLEMENT.
... one of the sides of a hexa- gon inscribed in the given circle . Let abd be a trigon inscribed in the given circle abde , and let the line de be one of the sides of a hexagon inscribed in the given circle ; then will 26 A NEW SUPPLEMENT.
Página 27
Joseph Denison. a hexagon inscribed in the given circle ; then will the square de- scribed upon ad , one of the sides of the trigon adb , be triple the square described upon de , one of the sides of the hexagon . By Proposition 10 ...
Joseph Denison. a hexagon inscribed in the given circle ; then will the square de- scribed upon ad , one of the sides of the trigon adb , be triple the square described upon de , one of the sides of the hexagon . By Proposition 10 ...
Página 53
... hexagon , and abc a trigon , both inscribed in the given circle abcd ; The hexagon aebfcd is dou- ble of the trigon abc . e h f 9 d Bisect each of the angles in the trigon by the lines bg , gc , and ga : these lines will meet in the ...
... hexagon , and abc a trigon , both inscribed in the given circle abcd ; The hexagon aebfcd is dou- ble of the trigon abc . e h f 9 d Bisect each of the angles in the trigon by the lines bg , gc , and ga : these lines will meet in the ...
Página 54
... hexagon ( Proposition 11 , Supple- ment ) ; also , because cgb is an angle of 120 ° , and that the triangle gbc is isosceles , the square of the side bc is triple of the square of the side bg ; wherefore the side bf is equal to the side ...
... hexagon ( Proposition 11 , Supple- ment ) ; also , because cgb is an angle of 120 ° , and that the triangle gbc is isosceles , the square of the side bc is triple of the square of the side bg ; wherefore the side bf is equal to the side ...
Página 55
... hexagon aebfcd ; wherefore the hexagon aebfcd is double of the trigon abc ; wherefore the hexagon , & c.— TO EUCLID'S ELEMENTS . 55.
... hexagon aebfcd ; wherefore the hexagon aebfcd is double of the trigon abc ; wherefore the hexagon , & c.— TO EUCLID'S ELEMENTS . 55.
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A New Supplement to Euclid's Elements of Geometry, by the Author of 'a New ... Joseph Denison Sin vista previa disponible - 2015 |
Términos y frases comunes
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
Pasajes populares
Página 62 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Página 5 - The areas of two similar triangles are to one another as the squares of their homologous or similarly situated sides (fig.
Página 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.
Página 63 - Ratios that are the same to the same ratio, are the same to one another.
Página 39 - F is of B, and that magnitudes have the same ratio to one another which their equimultiples have; (v.
Página 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.
Página 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...
Página 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.
Página 63 - CE equal to the ratio of the square of AB to the square of AD.
Página 61 - And in continued proportions, the square of the mean is equal to the rectangle contained by the extremes.