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 5
... ment , that the squares of any two right lines are to each other in the duplicate ratio of the two right lines , there being no demonstration of that important property in all the Elements . By means of that proposition the nineteenth ...
... ment , that the squares of any two right lines are to each other in the duplicate ratio of the two right lines , there being no demonstration of that important property in all the Elements . By means of that proposition the nineteenth ...
Página 6
... ment and observation that the spaces described by a heavy body in different times are as the squares of the times . Therefore let abc , ade be two similar triangles , of which ab , ad are homologous sides ; and let ab be equal to bd ...
... ment and observation that the spaces described by a heavy body in different times are as the squares of the times . Therefore let abc , ade be two similar triangles , of which ab , ad are homologous sides ; and let ab be equal to bd ...
Página 32
... ment ) ; and from the point a b 9 b , in the right line ab , draw bd perpendicular to ab , and meeting ac in the point d ( 1 Euclid , 11 ) . Also , at the point d in the line ad , make the angle ade containing 30 ° ( Proposition 14 ...
... ment ) ; and from the point a b 9 b , in the right line ab , draw bd perpendicular to ab , and meeting ac in the point d ( 1 Euclid , 11 ) . Also , at the point d in the line ad , make the angle ade containing 30 ° ( Proposition 14 ...
Página 33
... ment ) ; wherefore the line eb is half of the line . eg , and is equal to half of the equal side ed . And because each of the angles ead , eda at the base ad of the triangle aed contains 30 ° , the side ae is equal to the side ed ; but ...
... ment ) ; wherefore the line eb is half of the line . eg , and is equal to half of the equal side ed . And because each of the angles ead , eda at the base ad of the triangle aed contains 30 ° , the side ae is equal to the side ed ; but ...
Página 39
... ment ) ; wherefore ( 5 Euclid , 11 ) the sums of the sides are as the diameters . - Q . E. D. PROPOSITION XX . - THEOREM . The circumferences of circles are to each other as the diameters of the circles . Let the circumference of one of ...
... ment ) ; wherefore ( 5 Euclid , 11 ) the sums of the sides are as the diameters . - Q . E. D. PROPOSITION XX . - THEOREM . The circumferences of circles are to each other as the diameters of the circles . Let the circumference of one of ...
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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.