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 13
... circumference . PROPOSITION III . - PROBLEM . Within a given circle to draw a chord , the square of which chord shall be equal to the square of the radius . Let abd be the given circle and ac its radius TO EUCLID'S ELEMENTS . 13.
... circumference . PROPOSITION III . - PROBLEM . Within a given circle to draw a chord , the square of which chord shall be equal to the square of the radius . Let abd be the given circle and ac its radius TO EUCLID'S ELEMENTS . 13.
Página 14
... circumference of the cir- cle abd , the right line ab ( by the definition above ) is a chord of ( that is , within ) the circle ; and because the triangle abc is equilateral , the side ( that is , the chord ) ab is equal to the side ...
... circumference of the cir- cle abd , the right line ab ( by the definition above ) is a chord of ( that is , within ) the circle ; and because the triangle abc is equilateral , the side ( that is , the chord ) ab is equal to the side ...
Página 24
... circumference of the circle abd are radii of that circle , the lines cd and ch are equal , and the angles cdb and cbd at the base ab of the isosceles triangle bed are equal ; but it has been demonstrated that the angle cdb is 30 ...
... circumference of the circle abd are radii of that circle , the lines cd and ch are equal , and the angles cdb and cbd at the base ab of the isosceles triangle bed are equal ; but it has been demonstrated that the angle cdb is 30 ...
Página 26
... circumference , = 60 ° × 2 = 120 ° . And because the sides ac , cb of the triangle acb are radii of the circle abd , these sides are equal , and the triangle acb is an isosceles triangle whose vertical angle contains 120 ° . Wherefore ...
... circumference , = 60 ° × 2 = 120 ° . And because the sides ac , cb of the triangle acb are radii of the circle abd , these sides are equal , and the triangle acb is an isosceles triangle whose vertical angle contains 120 ° . Wherefore ...
Página 39
... circumferences of circles are to each other as the diameters of the circles . Let the circumference of one of the circles consist of the infinitely small sides of a polygon inscribed in it ; whatever be the number of sides of this ...
... circumferences of circles are to each other as the diameters of the circles . Let the circumference of one of the circles consist of the infinitely small sides of a polygon inscribed in it ; whatever be the number of sides of this ...
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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.