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 4
... line ; and , in the result , he found that the square of the line ad , being one of the sides of an equilateral tri ... given any general pro- blem for dividing an angle into any number what- ever of equal parts or angles . It appeared ...
... line ; and , in the result , he found that the square of the line ad , being one of the sides of an equilateral tri ... given any general pro- blem for dividing an angle into any number what- ever of equal parts or angles . It appeared ...
Página 12
... lines cd and ce , which was to be done . Note . - A right - angle contains ninety parts or degrees , expressed thus ... given point in a given right line to make a rectilineal angle of 120 ° . Let ab be the given right line , and a 12 A ...
... lines cd and ce , which was to be done . Note . - A right - angle contains ninety parts or degrees , expressed thus ... given point in a given right line to make a rectilineal angle of 120 ° . Let ab be the given right line , and a 12 A ...
Página 13
Joseph Denison. Let ab be the given right line , and a the given point in it ; it is required to make an angle of 120 ° at the given point a . b Upon the given line ab , describe the equilateral triangle abc ; and upon the side ac ...
Joseph Denison. Let ab be the given right line , and a the given point in it ; it is required to make an angle of 120 ° at the given point a . b Upon the given line ab , describe the equilateral triangle abc ; and upon the side ac ...
Página 14
... given circle abd , the square of which chord ab is equal to the square of the radius ac . Because the triangle acb is equilateral , the side cb is equal to the side ac , that is , to the radius ac ; and because the point c in the line ...
... given circle abd , the square of which chord ab is equal to the square of the radius ac . Because the triangle acb is equilateral , the side cb is equal to the side ac , that is , to the radius ac ; and because the point c in the line ...
Página 15
... given circle abd , is equal to the square of the radius ac . Wherefore within the given circle , & c . , which was ... line ce ( by 1 Euclid , 9 ) , cutting the line ab in e . From the point a as a centre , and at the dis- tance ae ...
... given circle abd , is equal to the square of the radius ac . Wherefore within the given circle , & c . , which was ... line ce ( by 1 Euclid , 9 ) , cutting the line ab in e . From the point a as a centre , and at the dis- tance ae ...
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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.